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2. Finite element analysis of pulse sharpening effect of gyromagnetic nonlinear transmission line based on Landau–Lifshitz–Gilbert equation.
- Author
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Zhang, Wenbin, Lin, Munan, Li, Haibo, and Qi, Xin
- Subjects
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FINITE element method , *ELECTRIC lines , *NONLINEAR analysis , *MAGNETIC moments , *MAGNETIC fields , *EQUATIONS - Abstract
Ferrite-loaded gyromagnetic nonlinear transmission line (GNLTL) provides a possible option to compress an input pulse to a narrower width for its remarkable sharpening effect. However, it is difficult to accurately predict the output of the GNLTL due to the complex interaction between the magnetic moment of ferrite and the bias magnetic field. In this paper, a finite element model of the GNLTL is established based on the Landau–Lifshitz–Gilbert equation to investigate the performance of the GNLTL. To validate this model, a prototype is used for experimental comparison. The result demonstrates good agreement between experiment and simulation. This paper further explores the influence of the bias magnetic field and the length of the GNLTL on the output pulse. Moreover, a method to sharpen the falling edge is proposed based on the reflection and superposition of the GNLTL output. Simulation and experimental results show its effectiveness and feasibility. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Free electron laser saturation: Exact solutions and logistic equation.
- Author
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Curcio, A., Dattoli, G., Di Palma, E., and Pagnutti, S.
- Subjects
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FREE electron lasers , *ELLIPTIC functions , *NONLINEAR oscillators , *EQUATIONS - Abstract
Models attempting an analytical description of free-electron laser (FEL) devices have been proposed in the past. They provided interesting results, leading either to a deeper understanding of the FEL dynamics and to semi-analytical formulae, useful for the preliminary design of self amplified spontaneous emission and oscillator FELs. Most of these models work well until the level of mild saturation. In this paper, we comment on the so-called logistic model and a more recent analysis describing the FEL evolution in terms of Jacobi elliptic functions. Both models are shown to be suited to describe the evolution from the low signal to the onset of saturation. We attempt therefore an extension of these theoretical formulations using a delayed logistic model, capable of including characteristic features like the post saturation power oscillations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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4. Bounded solutions of discrete equations with several fractional differences.
- Author
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Baštinec, Jaromír and Diblík, Josef
- Subjects
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EQUATIONS - Abstract
In the paper is considered a fractional discrete equation ∑ π = 1 s Δ β π z (k + 1) = G k (k , z (k) , ... z (k 0)) , k = k 0 , k 0 + 1 , ... where Δβπ, βπ > 0, π = 1, ...s, are the βπ order fractional differences, Gk:{k} × ℝ k-k0+1 → ℝ, k0 ∈ ℤ, k ∈ ℤ , k ≥ k0 and z: {k0, k0 + 1...} → ℝ. Sufficient conditions are given for the existence of bounded solutions satisfying inequalities b(k) < z(k) < c(k), ∀k ≥ k0 where b and c are real functions satisfying b(k) < c(k). An application is considered to an equation with several fractional differences ∑ π = 1 s Δ β π z (k + 1) = ξ z (k) + σ (k) , k = k 0 , k 0 + 1 , ... where ξ ∈ ℝ and σ:{k0, k0 + 1...} → ℝ. It is proved that there exists a bounded solution satisfying the inequality |z(k)| < L, k = k0, k0 + 1, ..., for a constant L. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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5. Bounded particular solution of a non-homogeneous system of two discrete equations.
- Author
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Baštinec, Jaromír and Diblík, Josef
- Subjects
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DISCRETE systems , *LINEAR systems , *EQUATIONS , *INTEGERS - Abstract
In the paper we consider a two-dimensional linear non-homogeneous system of discrete equations y 1 (k + 1) = a y 1 (k) + p y 2 (k) + g 1 (k) , y 2 (k + 1) = − q y 1 (k) + a y 2 (k) + g 2 (k) , where k = k0, k0 + 1,... with k0 a fixed integer, a, p > 0, q > 0 are real constants and gi: {k0, k0 + 1,...} ℝ, i = 1, 2 are given functions. Sufficient conditions are derived guaranteeing the existence of a solution y(k) = (y1(k), y2(k)), k = k0, k0 + 1, ... satisfying α y 1 2 (k) + β y 2 2 (k) < M , where M, α and β are positive fixed constants such that αp = βq. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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6. Distributed-order relaxation-oscillation equation.
- Author
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Rodrigues, M. M., Ferreira, M., and Vieira, N.
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EQUATIONS , *CAUCHY problem - Abstract
In this short paper, we study the Cauchy problem associated with the forced time-fractional relaxation-oscillation equation with distributed order. We employ the Laplace transform technique to derive the solution. Additionally, for the scenario without external forcing, we focus on density functions characterized by a single order, demonstrating that under these conditions, the solution can be expressed using two-parameter Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Analysis of the control set for the generalized Rayleigh equation.
- Author
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Ekimov, A. V., Balykina, Yu. E., and Svirkin, M. V.
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NONLINEAR functions , *EQUATIONS , *GENERALIZED estimating equations - Abstract
The paper considers generalized Rayleigh equation with control. A parametric analysis of the self-oscillating properties of this equation with zero control is carried out both for the case of a linear and for the case of a non-linear conservative function. Sufficient conditions for complete controllability of the corresponding system are obtained. In connection with the discontinuous dependence of the controllability set on the parameter, the corresponding value of the parameter is estimated, and the corresponding lower bound is constructed for the bounded controllability set. [ABSTRACT FROM AUTHOR]
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- 2024
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8. Periodic weak solutions for the quasi-linear parabolic chafee-infante equation by fixed point theorem.
- Author
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Hameed, Raad Awad, Tawfik, Israa Munir, and Talab, Shaimaa Rasheed
- Subjects
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NEUMANN boundary conditions , *EQUATIONS - Abstract
The authors of this manuscript have worked to investigate the existence of the time periodic weak solution Quasi-linear Chafee-Infante Equation with periodic initial conditions and Neumann boundary conditions. Since the equation our paper is degenerate, so we first need to establish the regular problem. By using Moser iteration technique, we establish a priori upper bound of the weak solution by using a good method that is called the Moser iteration technique. Then by usig the way of contradiction, we get a priori lower bound of the weak solution. This paper is based mainly on the fixed point theorem of infinite spaces, where we used the Leray–Schauder theory to investigate the existence of a non-trivial non-negative time periodic weak solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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9. Heat effects on supersonic jet screech: a linear stability analysis based on parabolized stability equations.
- Author
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Li, Binhong, Xu, Jiali, and Lyu, Benshuai
- Subjects
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MACH number , *LINEAR statistical models , *EULER equations , *LINEAR equations , *EQUATIONS , *EULER-Lagrange equations - Abstract
In this paper, we use the parabolized stability equations (PSEs) to investigate heat effects on supersonic jet screech. The PSE is derived from the linear Euler equations, and the computations are performed on an empirical mean flow profile. Employing PSE, we can examine several important characteristics of the shear-layer instability waves, including the convection velocity, the growth rate, and the location where the instability waves attain the maximal total amplification. Equipped with these knowledge, we further explore their impacts on the jet screech. Specifically, using a newly proposed iteration scheme, we first identify a more suitable convective Mach number to predict the screech frequency in both heated and cold jets. Second, we find that the transition of the screech mode from the axisymmetric to the helical mode may be explained by the shift in the most amplified instability modes. Using this criterion, we can predict a transition Mach number for the mode staging. Third, by assuming that the effective source location is the position where the instability wave attains its maximal amplitude and using the newly obtained convective Mach number, we can predict the screech mode staging in cold and heated jets using Gao's model. The predictions agree well with the experimental data. Finally, we investigate the heat effects on screech amplitude. It is found that compared to cold jets, the difference between the frequency of the most amplified instability wave and the frequency of the jet screech is much bigger in heated jets, which may lead to a lower screech amplitude. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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10. Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn.
- Author
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Li, Zhiyu, Song, Xiaomin, He, Gang, and Shu, Ji
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EQUATIONS , *DELAY differential equations , *PROBABILITY theory , *MEASUREMENT - Abstract
This paper is concerned with periodic measures of fractional stochastic complex Ginzburg–Landau equations with variable time delay on unbounded domains. We first derive the uniform estimates of solutions. Then we establish the regularity and prove the equicontinuity of solutions in probability, which is used to prove the tightness of distributions of solutions. In order to overcome the non-compactness of Sobolev embeddings on unbounded domains, we use the uniform estimates on the tails in probability. As a result, we prove the existence of periodic measures by combining Arzelà-Ascoli theorem and Krylov-Bogolyubov method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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11. KAM tori for two dimensional completely resonant derivative beam system.
- Author
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Xue, Shuaishuai and Sun, Yingnan
- Subjects
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TORUS , *EQUATIONS - Abstract
In this paper, we introduce an abstract KAM (Kolmogorov–Arnold–Moser) theorem. As an application, we study the two-dimensional completely resonant beam system under periodic boundary conditions. Using the KAM theorem together with partial Birkhoff normal form method, we obtain a family of Whitney smooth small–amplitude quasi–periodic solutions for the equation system. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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12. Bifurcations of degenerate homoclinic solutions in discontinuous systems under non-autonomous perturbations.
- Author
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Hua, Duo and Liu, Xingbo
- Subjects
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LYAPUNOV-Schmidt equation , *DIFFERENTIAL equations , *EQUATIONS - Abstract
The main aim of this paper is to study bifurcations of bounded solutions from a degenerate homoclinic solution for discontinuous systems under non-autonomous perturbations. We use Lyapunov–Schmidt reduction to give bifurcation equations and prove that a single parameter is enough to unfold two distinct homoclinic solutions bifurcated from the unperturbed degenerate homoclinic solution. Furthermore, we give an example of a periodically perturbed piecewise smooth differential equation in R 4 to support our conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
13. Effects of multiplicative noise on the fractional Hartree equation.
- Author
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Xie, J., Yang, H., and Wang, F.
- Subjects
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NOISE , *EQUATIONS , *CAUCHY problem - Abstract
This paper is dedicated to radial solutions to the Cauchy problem for the fractional Hartree equation with multiplicative noise. First, we establish a stochastic Strichartz estimate related to the fractional Schrödinger propagator. Local well-posedness for the Cauchy problem is proved by using stochastic and radial deterministic Strichartz estimates. Then, based on Itô's formula and stopping time arguments, the existence of a global solution is studied. Finally, we investigate the blow-up phenomenon and give a criterion via localized virial estimates. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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14. Global well-posedness for 2D non-resistive MHD equations in half-space.
- Author
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Zhang, Zhaoyun and Zhao, Xiaopeng
- Subjects
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NEUMANN boundary conditions , *BOUNDARY value problems , *INITIAL value problems , *EQUATIONS - Abstract
This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the non-resistive MHD equations have a unique global strong solution around the equilibrium state (0, e1) for Dirichlet boundary condition of velocity and modified Neumann boundary condition of magnetic. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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15. Almost oscillatory solutions of Emden-Fowler type neutral delay equations of third order.
- Author
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Saad, Jihan and Mohamad, Hussain Ali
- Subjects
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DELAY differential equations , *DIFFERENTIAL equations , *EQUATIONS - Abstract
In this paper, the asymptotic behavior and oscillation criteria of neutral differential equations of Emden-Fowler type of third order are studied. Where some conditions were formulated to ensure oscillation for all solutions of these equations. The obtained conditions can be generalized to higher order delay differential equations of Emden-Fowler type. The obtained results showed that the Emden-Fowler type in the neutral differential equation plays a major role in the presence or absence of the oscillation property, unlike other types of neutral differential equations. Some examples are presented to illustrate and apply the results obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. On exact solutions, conservation laws and invariant analysis of Rosenau-Hyman equation with generalized coefficients.
- Author
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Kumari, Pinki, Gupta, R. K., Kumar, Sachin, and Almusawa, Hassan
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CONSERVATION laws (Physics) , *CONSERVATION laws (Mathematics) , *NONLINEAR equations , *EQUATIONS , *DEPENDENT variables , *SYMMETRY - Abstract
In this paper, the nonlinear Rosenau-Hyman equation with time dependent variable coefficients is considered for inves-tigating its invariant properties, exact solutions and conservation laws. Using Lie classical method, we derive point symmetries admitted by the governing equation. Symmetry reductions are performed for each components of optimal set. Also nonclassical approach is employed to find some additional supplementary symmetries and corresponding symmetry reductions are performed. Later three kinds of exact solutions of considered equation are presented graphically for different parameters. In addition, local conservation laws are constructed for the considered equation by multiplier approach. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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17. Existence of weak solution to nonlinear parabolic type diffusion-convection-reaction equation.
- Author
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Aal-Rkhais, Habeeb Abed Kadhim
- Subjects
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TRANSPORT equation , *DEGENERATE parabolic equations , *DIRICHLET problem , *POROUS materials , *EQUATIONS , *GAS engineering - Abstract
The nonlinear parabolic type diffusion-convection processes with a source applied in many areas of science and engineering such as filtration of gas or fluid in porous media are considered. The aim of this paper is to concentrate on the existence of the weak solutions and boundary regularity for the Dirichlet problem of the degenerate parabolic equations in irregular domains in some cases where both the convection and reaction terms have the same exponents. The notion of parabolic modulus has a significant role in the boundary continuity of the solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
18. A numerical study of an exponential finite differences method with Grünwald–Letnikov derivatives for solving the fractional Korteweg-de Vries-Burger equation.
- Author
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Hamed, Almutasim Abdulmuhsin and Al-Rawi, Ekhlass S.
- Subjects
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FINITE difference method , *EQUATIONS , *NONLINEAR equations - Abstract
In this research, an algorithm was proposed for solving the nonlinear fractional space Korteweg-de Vries-Burger equation (NFSKDV-B) by an exponential finite difference method. The paper solves the NFSKDV-B equation at a fractional nonlinear space derivative with a suggested treatment to find apparent points outside the solution area. The numerical results compare the proposed analytic solution using absolute and mean square errors. The well-known shifted Grünwald–Letnikov (G-L) formula will approximate the fractional derivatives. Two examples were used as test problems to compare with the exact solution. This scheme found excellent agreement between the exact solution and the approximate solution. When compared to the exact solution, the approximate numerical solution is still very accurate, especially when the viscosity parameter is low. The results show how well the proposed method works with different values of fractional derivatives. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Asymptotic behavior of solutions for a doubly nonlinear parabolic non-divergence form equation with density.
- Author
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Aripov, Mersaid and Bobokandov, Makhmud
- Subjects
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NUMERICAL solutions to differential equations , *DEGENERATE parabolic equations , *CAUCHY problem , *NONLINEAR equations , *DENSITY , *EQUATIONS - Abstract
In this paper, we study the conditions of the Fujita type global solvability of solutions the Cauchy problem to double nonlinear degenerate parabolic equation with variable density and time dependent nonlinear source. The asymptotic properties of self-similar solution and the numerical analysis of considered problem including the critical and singular cases discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Nonlocal boundary value problems for a third order equation of elliptic-hyperbolic type.
- Author
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Islomov, Bozor and Usmonov, Bakhtiyor
- Subjects
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BOUNDARY value problems , *SINGULAR integrals , *OPERATOR equations , *EXISTENCE theorems , *EQUATIONS - Abstract
In this paper, we study nonlocal boundary value problems for a third-order equation with an elliptic-hyperbolic operator in the principal part. Existence and uniqueness theorems for the classical solution of the stated problems are proved. The proofs of the theorem are based on energy identities, as well as on the theory of singular and Fredholm integral equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. A 2D inverse problem for a fractional-wave equation.
- Author
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Rahmonov, Askar, Durdiev, Durdimurod, and Akramova, Dilshoda
- Subjects
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INVERSE problems , *EQUATIONS , *INTEGRAL equations , *WAVE equation - Abstract
In this paper, we consider two dimensional inverse problem for a fractional-wave equation with variable coefficient. The inverse problem is reduced to the equivalent integral equation. For solving this equation, the contracted mapping principle is applied. The local existence and global uniqueness results are proven. Also, the stability estimate is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Solving Newell-Whitehead-Segel, Stefan and nonlinear gas dynamics equations via modified Laplace variational iteration technique.
- Author
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Jneid, Maher
- Subjects
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GAS dynamics , *EQUATIONS , *ANALYTICAL solutions - Abstract
In this paper, a modification of variational iteration method (MVIM) is introduced for obtaining an approximate analytical solution of Newell-Whitehead-Segel equation, Stefan equation, and nonlinear gas dynamics equation. The proposed technique is an elegant combination of Laplace transform (LT) and He's variational iteration. This is been achieved by applying Laplace transform on the given PDEs then using He's variational iteration on the resulting system. Hence, we use the inverse Laplace transform at this step to get the required solution. This approach inserts a powerful and a reliable tool to obtain an analytical and approximate solution of the given PDEs. We implement this technique on Three numerical examples to show the effectiveness of this present method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Development of universal OCDMA DW code family equation and structure.
- Author
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Ammar, Syed Mohammad, Ali, Norshamsuri, Mohamad Saad, Mohamad Naufal, Bin Syed Junid, Syed Alwee Aljunid, and Endut, Rosdisham
- Subjects
- *
EQUATIONS - Abstract
OCDMA is one of the promising optical access technologies because of its notable characteristics, including asynchronous access and enhanced security. In this paper, the author introduced a new universal equation for the DW coding family The universal DW code equation allows for the construction of a new code structure, with either even (EW) or odd (OW) code weights. Contrast this with the previous formula, which contains separate equations for even and odd weights. Double Weight code has a fixed weight value of 2. EW and OW codes are variants of the Double Weight (DW) code family with weights above two. OW is unevenly weighted, while EW is evenly weighted. EW and OW were implemented in transmission connections to reduce noise and Multiple Access Interference (MAI). The revised equations for EW and OW can be used to calculate performance in order to measure the effectiveness of the code. Combining the current MDW and EDW codes yields the new equation. OW performs much better than the Hadamard, MFH, EW, and DW codes. OW can accommodate more than eighty concurrent users. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Efficient numerical method for model kinetic equations as applied to pulsed laser ablation into vacuum.
- Author
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Titarev, V. A. and Morozov, A. A.
- Subjects
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LASER ablation , *DISTRIBUTION (Probability theory) , *PULSED lasers , *EQUATIONS , *VELOCITY - Abstract
The paper is devoted to the construction of the efficient numerical methods to solve model kinetic equations as applied to the pulsed laser ablation (evaporation) into vacuum. We briefly describe the general ALE-type discrete velocity method and outline the modifications required for the present study. Then, we compute a particular moderate-intensity flow using Nesvetay code and compare the results for time-of-flight distributions and average axial energies with those of the DSMC code LasInEx. An accurate calculation of these quantities involves integration of the velocity distribution function in very narrow conical parts of the molecular velocity space and therefore requires the usage of a specially constructed mixed-element unstructured velocity mesh. Good agreement confirms the robustness and accuracy of the proposed discrete velocity approach. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Quasiclassical approaches to the generalized quantum master equation.
- Author
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Amati, Graziano, Saller, Maximilian A. C., Kelly, Aaron, and Richardson, Jeremy O.
- Subjects
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QUASI-classical trajectory method , *EQUATIONS of motion , *QUANTUM theory , *EQUATIONS , *STATISTICAL correlation , *LANGEVIN equations , *KERNEL functions - Abstract
The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin–boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
26. Normalized solutions for Kirchhoff–Choquard type equations with different potentials.
- Author
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Liu, Min and Sun, Rui
- Subjects
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EQUATIONS , *EQUATIONS of state - Abstract
In this paper, we are concerned with a Kirchhoff-Choquard type equation with L2-prescribed mass. Under different cases of the potential, we prove the existence of normalized ground state solutions to this equation. To obtain the boundedness from below of the energy functional and the compactness of the minimizing sequence, we apply the Gagliardo-Nirenberg inequality with the Riesz potential and the relationship between the different minimal energies corresponding to different mass. We also extend the results to the fractional Kirchhoff-Choquard type equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. Exact periodic solution family of the complex cubic-quintic Ginzburg–Landau equation with intrapulse Raman scattering.
- Author
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Zhou, Yuqian, Zhang, Qiuyan, Li, Jibin, and Yu, Mengke
- Subjects
- *
RAMAN scattering , *EQUATIONS , *NONLINEAR dynamical systems - Abstract
In this paper, we consider the exact solutions of the complex cubic-quintic Ginzburg–Landau equation. By investigating the dynamical behavior of solutions of the corresponding traveling wave system of this PDE, we derive exact explicit parametric representations of the periodic wave solutions under given parameter conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. On the physical vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation.
- Author
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Li, Kelin and Wang, Yuexun
- Subjects
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SHALLOW-water equations , *POISSON'S equation , *WATER depth , *EQUATIONS - Abstract
This paper is concerned with the vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation. We establish the local-in-time well-posedness of classical solutions to this system, and the solutions possess higher-order regularity all the way to the vacuum free boundary, though the density degenerates near the vacuum boundary. To deal with the force term generated by the Poisson equation, we make use of the structure of the momentum equation formulated in a fixed domain by the Lagrangian coordinates. The proof is built on some higher-order weighted energy functionals and weighted embeddings corresponding to the degeneracy near the initial vacuum boundary. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Uniqueness of conservative solutions to the modified Camassa-Holm equation via characteristics.
- Author
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He, Zhen and Yin, Zhaoyang
- Subjects
- *
CONSERVATIVES , *EQUATIONS - Abstract
In this paper, for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get the uniqueness of the conservative solution in the original variables. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Dynamical and statistical features of soliton interactions in the focusing Gardner equation.
- Author
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Zhang, Xue-Feng, Xu, Tao, Li, Min, and Zhu, Xiao-Zhang
- Subjects
- *
SOLITONS , *YANG-Baxter equation , *EXTREME value theory , *EQUATIONS , *DEGENERATE differential equations , *KURTOSIS - Abstract
In this paper, the dynamical properties of soliton interactions in the focusing Gardner equation are analyzed by the conventional two-soliton solution and its degenerate cases. Using the asymptotic expressions of interacting solitons, it is shown that the soliton polarities depend on the signs of phase parameters, and that the degenerate solitons in the mixed and rational forms have variable velocities with the time dependence of attenuation. By means of extreme value analysis, the interaction points in different interaction scenarios are presented with exact determination of positions and occurrence times of high transient waves generated in the bipolar soliton interactions. Next, with all types of two-soliton interaction scenarios considered, the interactions of two solitons with different polarities are quantitatively shown to have a greater contribution to the skewness and kurtosis than those with the same polarity. Specifically, the ratios of spectral parameters (or soliton amplitudes) are determined when the bipolar soliton interactions have the strongest effects on the skewness and kurtosis. In addition, numerical simulations are conducted to examine the properties of multi-soliton interactions and their influence on higher statistical moments, especially confirming the emergence of the soliton interactions described by the mixed and rational solutions in a denser soliton ensemble. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. Large time behavior for the Hall-MHD equations with horizontal dissipation.
- Author
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Shang, Haifeng
- Subjects
- *
BESOV spaces , *EQUATIONS - Abstract
This paper examines the large time behavior of solutions to the 3D Hall-magnetohydrodynamic equations with horizontal dissipation. As preparations we establish the global well-posedness of solutions and their global explicitly uniform upper bounds for Hk (k ≥ 1) to this system with initial data small in H2. Furthermore, if the initial data also belongs to homogeneous negative Besov spaces, we prove the optimal decay rates of the aforementioned global solutions and their higher order derivatives. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Including the parallel mass flow in calculating the steady-state solutions and stability of the momentum balance equations for a quasisymmetric stellarator.
- Author
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Michaelides, D. N. and Talmadge, J. N.
- Subjects
- *
STEADY-state flow , *MAGNETIC fields , *ION migration & velocity , *ELECTRIC fields , *EQUATIONS , *MOMENTUM (Mechanics) , *EIGENVECTORS - Abstract
The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. The Rossiter equation: Improving the fractional vortex speed and defining an effective length to depth ratio for cavity flows.
- Author
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Gabel, Matthew and Sarigul-Klijn, Nesrin
- Subjects
- *
MACH number , *COMPRESSIBLE flow , *EQUATIONS , *WALKING speed - Abstract
This paper first reviews well known analytical techniques for predicting the Rossiter modes of a cavity in compressible flow. We combine existing methods to improve the performance in compressible flow. Second, we introduce a method based on an effective length to depth ratio of the cavity from experimental results for predicting frequencies across Mach numbers. Finally, the fractional vortex speed used in the Rossiter equation and its derivatives is calculated from high subsonic (M 0.55) to supersonic (M 2.3) for use in future cavity mode prediction. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. The Fokker–Planck–Boltzmann equation in the finite channel.
- Author
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Lei, Yuanjie, Zhang, Jing, and Zhang, Xueying
- Subjects
- *
EQUATIONS , *MATHEMATICS - Abstract
In this paper, we establish the existence of small-amplitude unique solutions near the Maxwellian for the Fokker–Planck–Boltzmann equation in a finite channel with specular reflection boundary conditions. The solution space we consider is denoted as L k ̄ 1 L T ∞ L x 1 , v 2 , introduced in Duan et al. [Commun. Pure Appl. Math. 74(5), 932–1020 (2021)]. In addition, we investigate the long-time behavior of solutions for both hard and soft potentials. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Investigation of complex hyperbolic and periodic wave structures to a new form of the q-deformed sinh-Gordon equation with fractional temporal evolution.
- Author
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Abdel-Aty, Abdel-Haleem, Arshed, Saima, Raza, Nauman, Alrebdi, Tahani A., Nisar, K. S., and Eleuch, Hichem
- Subjects
- *
SYMMETRY breaking , *EQUATIONS , *ANALYTICAL solutions , *SINE-Gordon equation - Abstract
This paper presents the fractional generalized q-deformed sinh-Gordon equation. The fractional effects of the temporal derivative of the proposed model are studied using a conformable derivative. The analytical solutions of the governing model depend on the specified parameters. The resulting equation is studied with two integration architectures: the sine-Gordon expansion method and the modified auxiliary equation method. These strategies extract hyperbolic, trigonometric, and rational form solutions. For appropriate parametric values and different values of fractional parameter α, the acquired findings are displayed via 3D graphics, 2D line plots, and contour plots. The graphical simulations of the constricted solutions depict the existence of bright soliton, dark soliton, and periodic waves. The considered model is useful in describing physical mechanisms that possess broken symmetry and incorporate effects such as amplification or dissipation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. Breather wave solutions on the Weierstrass elliptic periodic background for the (2 + 1)-dimensional generalized variable-coefficient KdV equation.
- Author
-
Li, Jiabin, Yang, Yunqing, and Sun, Wanyi
- Subjects
- *
DARBOUX transformations , *NONLINEAR waves , *EQUATIONS , *EVOLUTION equations , *NONLINEAR evolution equations , *ELLIPTIC equations , *ELLIPTIC operators - Abstract
In this paper, the N th Darboux transformations for the (2 + 1) -dimensional generalized variable-coefficient Koretweg–de Vries (gvcKdV) equation are proposed. By using the Lamé function method, the generalized Lamé-type solutions for the linear spectral problem associated with the gvcKdV equation with the static and traveling Weierstrass elliptic ℘ -function potentials are derived, respectively. Then, the nonlinear wave solutions for the gvcKdV equation on the static and traveling Weierstrass elliptic ℘ -function periodic backgrounds under some constraint conditions are obtained, respectively, whose evolutions and dynamical properties are also discussed. The results show that the degenerate solutions on the periodic background can be obtained by taking the limits of the half-periods ω 1 , ω 2 of ℘ (x) , and the evolution curves of nonlinear wave solutions on the periodic background are determined by the coefficients of the gvcKdV equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2.
- Author
-
Ge, Chuanfang and Geng, Jiansheng
- Subjects
- *
QUINTIC equations , *NONLINEAR equations , *EQUATIONS - Abstract
In the present paper, we consider two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Because of this reversible system without external parameters or potentials, Birkhoff normal form reduction is necessary before applying Kolmogorov–Arnold–Moser (KAM) theorem. As application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proved in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
38. Depressed cubic equation over domain ℤ2*.
- Author
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Mohd Azahari, Mohammad Azim and Ahmad, Mohd Ali Khameini
- Subjects
- *
CUBIC equations , *POLYNOMIALS , *EQUATIONS - Abstract
The polynomial equations demand different solvability criterion in the p-adic field compared to the real field. This is due to the non-Archimedean and finite properties that been used in the p-adic field. In previous work, the solvability criterion of the cubic equations had been studied in depressed form for case p≥2. However, the proof for case prime p = 2 is not complete. This paper will provide the proof of such a problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Numerical computation of convection-diffusion-reaction equation using an improved explicit finite difference method.
- Author
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Mohd Supian, Nurhusnina, Rusli, Nursalasawati, and Kasiman, Erwan Hafizi
- Subjects
- *
TRANSPORT equation , *FINITE difference method , *EULER method , *CHEMICAL species , *EQUATIONS , *HEAT transfer - Abstract
The convection-diffusion-reaction equation is one of the most useful equations in predicting many physical and chemical phenomena such as heat transfer, chemical species transport and reaction and the pollutants adsorption in wastewater. The widely used Upwind Forward Euler method may produce a negative solution because a time step size value is more than 0.005 and may form numerical oscillations. An improvement in the proper selection of time step size values is suggested, which removes the numerical oscillation and significantly improves the accuracy and convergence of the solution. In this paper, we add two explicit finite difference methods: Forward Time Central Space (FTCS) and Lax-Friedrichs, together with the previous method, Upwind, to solve the convection-diffusion-reaction equation with the improvement of time step size. An example is drawn from the literature to test the results of the numerical methods. The exact solution is used for comparison. Finally, the Upwind method solves the convection-diffusion-reaction problem satisfactorily with the restricted time step size, while the FTCS and Lax method form unstable solutions and thus causes the methods to be inapplicable for solving the convection-diffusion-reaction equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. W-projective curvature tensor of nearly kahler manifold.
- Author
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Ali, Ali Khalaf and Shihab, A. A.
- Subjects
- *
CURVATURE , *SYMMETRY , *EQUATIONS - Abstract
In this paper we study the w-projective curvature tensor of nearly kahler manifold, i.e. The geometrical properties of one of the AH ("Almost Hermitian")-manifold structures are given by W1, where W1 indicates the almost Kahler manifold, and the w-Projective tensor of a nearly Kahler manifold has been examined in this research. The following are the important conclusions of the study:-The typical Riemannian curvature symmetry features of this tensor were demonstrated. In the NK-manifold, calculate the Projective tensor (W-tensor) components. Some observations were obtained, and links between the tensor components of this manifold were constructed. For these components w0, w1, w2, w3, w4, w5, w6, w7 of virtually kahler is haler manifold, provide a neutral equation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Energy stable symmetric interior penalty discontinuous Galerkin finite element for a growth Cahn-Hilliard equation.
- Author
-
Aristotelous, A. C.
- Subjects
- *
PARTIAL differential equations , *DISCONTINUOUS functions , *EQUATIONS - Abstract
In this paper we devise and analyze a symmetric interior penalty (SIP) discontinuous Galerkin (DG) finite element (FE) method for a growth Cahn-Hilliard equation (GCH) with a polynomial potential and (general) nonlinear growth term, equipped with homogeneous Dirichlet boundary conditions. The original partial differential equation (PDE) system is rewritten by introducing an extra variable, and it is shown to be a gradient flow of an energy functional, that its solutions dissipate. The proposed first order convex splitting (CS) fully discrete scheme is shown to be energy stable with respect to a spatially discrete analogue of the continuous free energy of the system. At the fully discrete level the energy law is shown to hold unconditionally with respect to the temporal discretization parameter and conditionally with respect to the spatial discretization parameter. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. On one boundedness related to the non-oscillating solutions of quasi-linear functional-differential equations of retarded type with nonlinear impulsive conditions.
- Author
-
Donev, V. I.
- Subjects
- *
IMPULSIVE differential equations , *FUNCTIONAL differential equations , *EQUATIONS - Abstract
This paper is dealing with first order quasi-linear functional-differential equation of delayed type with nonlinear impulsive conditions. It is shown that under certain conditions a boundedness is formed of the quotient between the solution of the equation at the present moment and the solution in its prehistory. The influence of this boundedness on the oscillation of all solutions of the considered equations is demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Electronic absorption spectra from off-diagonal quantum master equations.
- Author
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Lai, Yifan and Geva, Eitan
- Subjects
- *
ABSORPTION spectra , *ELECTRONIC spectra , *JAHN-Teller effect , *PERTURBATION theory , *SMALL states , *EQUATIONS of motion , *EQUATIONS - Abstract
Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. A key experimental quantity that relies on the ability to obtain accurate Schrödinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrödinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from the electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion method. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
44. A new algorithm of path planning in 3D environments for an implemented quadcopter robot.
- Author
-
Albaghdadi, Mustafa Fahem, Manaa, Mehdi Ebady, and Albaghdadi, Ahmed Fahem
- Subjects
- *
ROBOTS , *SPHERES , *EQUATIONS - Abstract
Path planning within three-dimensional environments is of great importance in contemporary time due to the introduction of robots in many works. Finding the shortest path reduces fuel and time. In this paper a new algorithm is proposed to plan the paths within 3D environments. The algorithm was tested in two ways: simulation and practical. A multi-propeller vehicle is built that can track the resulting path from the proposed algorithm. The spherical shape of the robot, and obstacles is the basic of the work of the proposed algorithm. This does not mean that the algorithm cannot handle other forms of obstacles. Any other shape can be represented by a set of intersecting spheres. The resulting path of this proposed algorithm consists of two pieces that can be repeated a number of times until reaching the target point. The first piece is a straight path connecting the current position of the robot with a point located on the edge of the obstacle. The second piece is a path around the obstacle connecting two points away from the obstacle with a distance equal to the radius of the robot. All points are calculated by equations derived in this paper. The proposed algorithm was compared with two other algorithms. The results proved the superiority of the proposed algorithm in terms of path length and smoothness of the path. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Global well-posedness and decay of the 2D incompressible MHD equations with horizontal magnetic diffusion.
- Author
-
Lin, Hongxia, Zhang, Heng, Liu, Sen, and Sun, Qing
- Subjects
- *
HEAT equation , *EQUATIONS , *MAGNETIC fields , *PHYSICAL constants - Abstract
This paper concerns two-dimensional incompressible magnetohydrodynamic (MHD) equations with damping only in the vertical component of velocity equations and horizontal diffusion in magnetic equations. If the magnetic field is not taken into consideration the system is reduced to Euler-like equations with an extra Riesz transform-type term. The global well-posedness of Euler-like equations remains an open problem in the whole plane R 2 . When coupled with the magnetic field, the global well-posedness and the stability for the MHD system in R 2 have yet to be settled too. This paper here focuses on the space domain T × R , with T being a 1D periodic box. We establish the global well-posedness of the 2D anisotropic MHD system. In addition, the algebraic decay rate in the H2-setting has also been obtained. We solve this by decomposing the physical quantity into the horizontal average and its corresponding oscillation portion, establishing strong Poincaré-type inequalities and some anisotropic inequalities and combining the symmetry conditions imposed on the initial data. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Normalized ground states for fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities.
- Author
-
Kong, Lingzheng and Chen, Haibo
- Subjects
- *
EQUATIONS - Abstract
In this paper, we study the existence of normalized ground states for nonlinear fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities in R 3 . To overcome the special difficulties created by the nonlocal term and fractional Sobolev critical term, we develop a perturbed Pohožaev method based on the Brézis–Lieb lemma and monotonicity trick. Using the Pohožaev manifold decomposition and fibering map, we prove the existence of a positive normalized ground state. Moreover, the asymptotic behavior of the obtained normalized solutions is also explored. These conclusions extend some known ones in previous papers. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. IV. Radial pressure.
- Author
-
Célérier, M.-N.
- Subjects
- *
MATHEMATICAL simplification , *ROTATING fluid , *DIFFERENTIAL equations , *FLUIDS , *EQUATIONS , *AZIMUTH - Abstract
This article belongs to a series where the influence of anisotropic pressure on gravitational properties of rigidly rotating fluids is studied using new exact solutions of GR constructed for the purpose. For mathematical simplification, stationarity and cylindrical symmetry implying three Killing vectors are considered. Moreover, two pressure components are set to vanish in turn. In Papers I and II, the pressure is axially directed, while it is azimuthal in Paper III. In present paper (Paper IV), a radially directed pressure is considered. Since a generic differential equation, split into three parts, emerges from field equations, three different classes of solutions can be considered. Two could only be partially integrated. The other one, which is fully integrated, yields a set of solutions with a negative pressure. Physical processes where a negative pressure is encountered are depicted and give a rather solid foundation to this class of solutions. Moreover, these fully integrated solutions satisfy the axisymmetry condition, while they do not verify the so-called "regularity condition." However, since their Kretschmann scalar does not diverge on the axis, this feature must be considered as reporting a mere coordinate singularity. Finally, the matching of these solutions to an exterior appropriate vacuum enforces other constraints on the two constant parameters defining each solution in the class. The results displayed here deserve to be interpreted in light of those depicted in the other four papers in the series. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Wronskian rational solutions to the generalized (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation in fluid dynamics.
- Author
-
Cheng, Li, Zhang, Yi, Ma, Wen-Xiu, and Hu, Ying-Wu
- Subjects
- *
FLUID dynamics , *BACKLUND transformations , *EQUATIONS , *ROGUE waves - Abstract
The main topic of the paper is to investigate the generalized (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) and Korteweg–de Vries (KdV) equations, which are widely used in many physical areas, especially in fluids. A new Wronskian formulation is presented for these two equations associated with the bilinear Bäcklund transformation. Based on Wronskian identities of the bilinear Kadomtsev–Petviashvili (KP) hierarchy, the Wronskian determinant solution is verified by a direct and concise calculation. The newly introduced Wronskian formulation provides a comprehensive way for building rational solutions. A few rational Wronskian solutions of lower order are computed for the generalized (2 + 1)-dimensional DJKM equation. Our work can show that the extended (2 + 1)-dimensional KdV equation possesses the similar rational Wronskian solutions through the corresponding logarithmic transformation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Application of the unified equation of bubble dynamics for simulating the large-scale air-gun bubble with migration effect.
- Author
-
Liu, Yi, Zhang, Shuai, Li, Shuai, and Zhang, A-Man
- Subjects
- *
BUBBLE dynamics , *EARTHQUAKE resistant design , *AIR guns , *FLOW velocity , *EQUATIONS - Abstract
How to effectively reduce the high-frequency output caused by excessively steep initial peak slope and enhance the low-frequency output generated by bubble oscillation has become present research interest in seismic source design. The most effective way to improve the low-frequency content of a seismic source is to increase its chamber volume. However, the size of air-gun bubbles generated by large-volume air-gun sources has increased by several hundred times compared to traditional high-pressure air guns, which has made the migration phenomenon of bubbles no longer negligible. The previous air-gun bubble dynamics models did not comprehensively account for the effects caused by bubble migration phenomenon. In this paper, we have developed an air-gun bubble dynamics model based on unified equation for bubble dynamics, and the newly established model demonstrates a closer alignment with experimental data compared to models based on the Gilmore and Keller equations. Based on this, the influence of the design parameters of air-gun seismic source on the bubble migration is studied. It explores the ramifications of migration on the dynamic properties of air-gun bubbles and the signatures of seismic sources. Additionally, we examine how incoming flow velocity magnitude and air-gun design parameters influence the signatures of air-gun seismic sources. Finally, we investigate the impact of both the spacing between dual guns and the horizontal movement of bubbles caused by mutual attraction on the signatures of dual-gun sources. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. Asymptotic analysis of the higher-order lump in the Davey-Stewartson I equation.
- Author
-
Guo, Lijuan, Zhu, Min, and He, Jingsong
- Subjects
- *
EQUATIONS , *DIAMONDS , *POLYNOMIALS , *EIGENVECTORS - Abstract
In this paper, the long-time asymptotic dynamics of three types of the higher-order lump in the Davey-Stewartson I equation, namely the linear lump, triangular lump and quasi-diamond lump, are investigated. For large time, the linear lump splits into certain fundamental lumps arranged in a straight line, which are associated with root structures of the first component in used eigenvector. The triangular lump consists of certain fundamental lumps forming a triangular structure, which are described by the roots of a special Wronskian that is similar to Yablonskii-Vorob polynomial. The quasi-diamond lump comprises a diamond in the outer region and a triangular lump pattern in the inner region (if it exists), which are decided by the roots of a general Wronskain determinant. The minimum values of these lump hollows are dependent on time and approach zero when time goes to infinity. Our approximate lump patterns and true solutions show excellent agreement. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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