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A new intrinsically-relativistic kinetic mechanism for generation of non-isotropic relativistic kinetic equilibria in collisionless N-body systems is pointed out. The theory is developed in the framework of the covariant Vlasov statistical description. The new effect is based on the constraints placed by the conservation laws of neutral single-particle dynamics in prescribed background curved-spacetimes demonstrating existence of Killing tensors. As an illustration, the particular case of the Kerr space-time admitting the so-called Carter constant for the particle geodesic motion is considered. The general functional form of the equilibrium kinetic distribution function (KDF) is determined and an explicit realization in terms of Gaussian-like distributions is provided. It is shown that, due to the Carter constant, these equilibrium KDFs exhibit an anisotropic phase-space functional dependence in terms of the single-particle 4-velocity components, giving rise to corresponding non-isotropic continuum fluid fields. The qualitative properties of the equilibrium stress-energy tensor associated with these systems are discussed, with a particular emphasis on the related occurrence of temperature anisotropy effects. The theory is susceptible of astrophysical applications, including in particular the statistical properties of dark matter halos around stellar-mass or galactic-center black holes., 14 pages

Heat and mass transfer analysis of viscous liquid flow generated by rotation of disk has generated prodigious interest due to promising utilizations in numerous processes such as thermal energy generation systems, turbine rotators, geothermal energy preservations, chemical processing, medicinal instrumentations, computing devices and so forth. In view of such extraordinary utilizations in numerous engineering procedures existent exertion is excogitated to disclose flowing phenomenon over rotating disk. To raise the importance of current analysis influential physical aspects like magnetic field, permeability, Dufour and Soret diffusion phenomenon are also incorporated. Subsequently, flow field distributions are analyzed for suction and injection cases. Modelling is structured via PDE’s by obliging constitutive conservation laws. Boundary layer approach is executed to reduce complexity of attained partial differential system. Transformations developed by Karman are implemented to convert developed differential framework into ODE’s. Implicitly finite differenced technique known as Keller Box is engaged to find solution of coupled intricate high order ordinary differential equations. Influence of flow controlling parameters on associated distributions are revealed through graphical and tabular representations. The related quantities of engineering interest like coefficients of wall drag force, along radial and tangential directions are also computed. Credibility of presently computed results is established by constructing comparison with previously published literature. It is inferred that magnetic strength parameter enhances tangential and radial components of velocity whereas contrary trend is depicted in axially directed velocity. In addition, temperature and momentum distributions show up surging attribute versus magnetic field parameter. All associated profiles have exhibited decrementing aspects against suction parameter. It is also revealed that increment in Soret tends to produce depreciation in temperature profile whereas concentration distribution is enhanced.

Starting from a 2 × 2 discrete matrix spectral problem, we construct an integrable lattice hierarchy associated with RTL + ( α ) system which is a one-parameter perturbation of the usual Toda lattice system describing the particle motion in a lattice. Based on the obtained RTL + ( α ) hierarchy, some integrable properties such as Hamiltonian structures, Liouville integrability and conservation laws are investigated. Furthermore, we establish the discrete N -fold Darboux transformation (DT) of RTL + ( α ) system. As applications of the obtained DT, multi-soliton solutions are derived on constant seed backgrounds, and discrete soliton propagation and elastic interaction structures are shown graphically and analyzed via asymptotic analysis. Numerical simulations are utilized to demonstrate the dynamical behaviors of such soliton solutions. Numerical results show that soliton evolutions are stable against a small noise. Results given in this paper might be helpful for understanding the propagation of nonlinear waves in soliton theory.

In this paper, we study a fourth-order nonlinear symmetric regularized long-wave equation which arises in several physical applications including ion sound waves in plasma. This model also describes nonlinear ion-acoustic and space-charge waves. Lie group analysis and the tanh-coth method is utilized for the construction of solitary wave solutions to the equation. Based on each symmetry, we reduce the considered partial differential equation into different ordinary differential equations. The obtained equations are solved and new solitary wave patterns are reported. To understand the physical interpretation, some solitary wave structures are exhibited graphically. Also, by using the multiplier approach, we constructed the local conservation laws of the considered equation.

The Mei symmetry and conservation laws for time-scale nonshifted Hamilton equations are explored, and the Mei symmetry theorem is presented and proved. Firstly, the time-scale Hamilton principle is established and extended to the nonconservative case. Based on the Hamilton principles, the dynamic equations of time-scale nonshifted constrained mechanical systems are derived. Secondly, for the time-scale nonshifted Hamilton equations, the definitions of Mei symmetry and their criterion equations are given. Thirdly, Mei symmetry theorems are proved, and the Mei-type conservation laws in time-scale phase space are driven. Two examples show the validity of the results.

В работе найдены законы сохранения для трехмерных стационарных уравнений упругости в случае общей анизотропии. Conservation Laws for 3-dimensional Stationary Equations in the Case of General Anosotropy are obtained in the work.

Solitary waves are usually outcome of nonlinear and dispersive effects. The Date–Jimbo–Kashiwara–Miwa equation is dispersive and highly nonlinear soliton equation. The Date–Jimbo– Kashiwara–Miwa equation is a well-known integrable generalization of the KP equation and represents evolution of propagating waves in nonlinear dispersive media. It has wave dispersion changing properties in nonlinear dynamics. In this work, we aim to carry out symmetry reductions and exact solutions of the Date–Jimbo–Kashiwara–Miwa equation using Lie point symmetries. The possible infinitesimal generators and infinite-dimensional algebra of symmetries are constructed by utilizing the invariance property of Lie groups. Then, similarity variables are used to reduce the test problem and lead to determining ordinary differential equations. These equations provide desired exact solutions under some parametric constraints. The derived solutions are generalized than previous established results and have never been reported yet. Moreover, the self-adjoint equation and conserved vectors with associated symmetries are established under the Lagrangian formulation. To demonstrate the significance of interaction phenomena, the solutions have been extended with numerical simulation. Consequently, stripe soliton, line soliton, multisoliton, soliton fission, parabolic profile and their elastic nature are discussed systematically to validate these solutions with physical phenomena.

In this paper, we will consider the wave-breaking mechanism and persistence property of the solution for the weakly dissipative shallow water equation. A wave breaking will arise as soon as the initial value decay faster than the solitary waves at infinity. Therefore, the wave-breaking phenomena is studied by three different methods we provided, which extends the information of this equation. Since the presence of the weakly dissipative term, the equation loses the conservation law $$E=\int _{\mathbb {R}}u^2+u_x^2\mathrm{d}x$$ . This difficulty has been solved by establishing the energy inequality. The main idea of the first two methods is to construct the Riccati-type differential inequality to show that the solution of the equation blows up in finite time. The last method depends on the introduction of two families of Lyapunov functions. In addition, we exhibit the persistence results of the solution in weighted $$L^p$$ -spaces.

In this paper, we consider coupled Korteweg-de Vries equations that model the propagation of shallow water waves, ion-acoustic waves in plasmas, solitons, and nonlinear perturbations along internal surfaces between layers of different densities in stratified fluids, for example propagation of solitons of long internal waves in oceans. The method of Lie group analysis is used to on the system to obtain symmetry reductions. Soliton solutions are constructed by use of a linear combination of time and space translation symmetries. Furthermore, we compute conservation laws in two ways that is by multiplier method and by an application of new conservation theorem developed by Nail Ibragimov.

On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical system of scalar charged fermions interacting by means of classical and phantom scalar fields. Based on the study of the microscopic dynamics of scalar charged particles, within the framework of the Lagrangian as well as Hamiltonian formalism, a function of the dynamic mass of scalar charged particles was constructed and it was shown that for the consistency of the theory, it is necessary to remove the nonnegativity condition for this function. On the basis of the Lagrangian formalism, equations of gravitational and scalar fields with singular sources are formulated and microscopic conservation laws are obtained. Within the framework of the general relativistic kinetic theory, macroscopic equations of gravitational and scalar fields are formulated and macroscopic conservation laws are obtained. These equations' full correspondence to microscopic equations with singular sources is shown. Further, on the basis of the obtained equations, a cosmological model for a degenerate system of scalarly charged fermions is formulated. An exact solution of the constitutive equations for a degenerate scalar-charged plasma in the cosmological model is obtained, which made it possible to significantly simplify the original system of equations. On the basis of the obtained solution of the constitutive equations, two fundamentally different cosmological models are formulated, one of which has two types of singly scalarly charged fermions, while the second has one kind of fermions charged with two charges of various nature. A qualitative analysis of the obtained 6-dimensional dynamic system for a two-component model is carried out., 31 pages, 70 references

A well-known problem in classical mechanics that is often presented for pedagogical purposes involves a small mass that slides without friction under a gravitational force on the surface of a sphere. Commonly, students are asked to find the angular position where a mass with no azimuthal motion leaves the spherical surface, and this question is easily within the reach of most intermediate physics students. However, a complete solution for more general motion of the mass on the spherical surface (including friction) may be suitable for many advanced undergraduates. Without friction, the problem including azimuthal motion is really an inverted version of an ideal spherical pendulum. This problem is also useful for extending discussion in classical mechanics to more sophisticated topics beyond solving Newton's laws of motion, such as the importance of conservation laws and constants of motion as they relate to symmetry, conservative versus dissipative forces, and the role of constraints.

Our paper is devoted for the study of a highly compact string-like axially symmetric object in the presence of electromagnetic field which is generated by the existence of electric charge in the model. The basic formulism of one of the alternative theories i.e, f ( R , G ) theory has been used for this purpose. We have considered the irrotational cylindrical geometry, influence of charge, isotropic pressure and the perfect fluid for the derivation of field equations and the laws of conservation corresponding to f ( R , G ) theory. Junction conditions suggested by Darmois-Israel will be used for the smooth matching between inner and outer regions of gravastar-like structure. The impact of electric charge on distinct physical features of the model such as proper length, energy, thickness and entropy of shell will also be observed and will be elaborated with the help of graphs. We shall also analyze the vital role of f ( R , G ) theory for the stability of the model.

Kepler’s laws are an appropriate topic to highlight the significance of the pedal equation in physics. There are several articles that obtain Kepler’s laws through conservation and gravitation laws. This can be shown more easily and ingeniously if one uses the pedal equation of an ellipse. In fact, the complete kinematics of a particle in an attractive central force field can be derived from one single pedal form. Though many articles use the pedal equation, the classical procedure (without proof) for obtaining the pedal equation is mentioned only in a few because the classical derivations can sometimes be lengthier and are not simple. In this paper, using elementary physics, we derive the pedal equation for all conic sections in a unique, short, and pedagogical way. Later, from the dynamics of a particle in the attractive central force field, we deduce the single pedal form, which elegantly describes all the possible trajectories. Also, for the purpose of completeness, we derive Kepler’s laws.

The coupled nonlocal NLS equation is studied by virtue of the $2\times2$ Dbar-problem. Two spectral transform matrices are introduced to define two associated Dbar-problems. The relations between the coupled nonlocal NLS potential and the solution of the Dbar-problem are constructed. The spatial transform method is extended to obtain the coupled nonlocal NLS equation and its conservation laws. The general nonlocal reduction of the coupled nonlocal NLS equation to the nonlocal NLS equation is discussed in detail. The explicit solutions are derived.

The complex interplay between thermal, hydrodynamic, and electromagnetic, forces governs the evolution of multi-phase systems in high technology applications, such as advanced manufacturing and fusion power plant operation. In this work, a new formulation of the time dependent magnetic induction equation is fully coupled to a set of conservation laws for multi-phase fluid flow, energy transport and chemical species transport that describes melting and solidification state transitions. A finite-volume discretisation of the resulting system of equations is performed, where a novel projection method is formulated to ensure that the magnetic field remains divergence free. The proposed framework is validated by accurately replicating a Hartmann flow profile. Further validation is performed through correctly predicting the experimentally observed trajectory of Argon bubbles rising in a liquid metal under varying applied magnetic fields. Finally, the applicability of the framework to technologically relevant processes is illustrated through the simulation of an electrical arc welding process between dissimilar metals. The proposed framework addresses an urgent need for numerical methods to understand the evolution of multi-phase systems with large electromagnetic property contrast.

10.1119/10.0004801.1We explore the forces and conservation laws that govern the motion of a hockey puck that slides without friction on a smooth, rotating, self-gravitating spheroid. The earth's oblate spheroidal shape (apart from small-scale surface features) is determined by balancing the gravitational forces that hold it together against the centrifugal forces that try to tear it apart. The earth achieves this shape when the apparent gravitational force on the puck, defined as the vector sum of the gravitational and centrifugal forces, is perpendicular to the earth's surface at every point on the surface. Thus, the earth's spheroidal deformations neutralize the centrifugal and gravitational forces on the puck, leaving only the Coriolis force to govern its motion. Motion on the spheroid therefore differs profoundly from motion on a rotating sphere, for which the centrifugal force plays a key role. Kinetic energy conservation reflects this difference: On a stably rotating spheroid, the kinetic energy is conserved in the rotating frame, whereas on a rotating sphere, it is conserved in the inertial frame. We derive these results and illustrate them using CorioVis software for visualizing the motion of a puck on the earth's spheroidal surface.

This article explores progressive solitary solution and shock solution for the dust–ion-acoustic waves (DIAWs) propagating in a collisional unmagnetized dusty plasma containing dust grains with negative dust charge, positive ions, neutral particles and Maxwellian electrons. In an earlier literature, Gao et al. in Braz. J. Phys. (2019) derived nonplanar KdV–Burgers (NKDVB) equation from the basic field equation utilizing reductive perturbation method (RPT). Further, assuming that conservation law holds in the system they obtained an approximate solitary wave solution, although the presence of Burgers term causes increase of the effect from viscosity and opposes the conservation law in the system. In that case, shock is wave usually generated due to the effect of strong anomalous dissipation. Being aware of the facts, simplified Hirota bilinear method is employed and shock-type wave solution is obtained. Again, if dissipation is weak, the balance between the dispersion and nonlinearity may lead to form solitary solution. Considering the case of weak dissipation, solitary wave solution is directly explored (without assuming conservation law) by applying a weighted residual method. Some 2D and 3D graphs are depicted to analyze the propagating behavior of nonplanar waves in different parametric spaces.

This paper implements a multiplier approach to exhibit conservation laws in magneto-optic waveguides that maintain anti-cubic as well as generalized anti-cubic forms of the nonlinear refractive index. Three conservation laws are retrieved for each form of nonlinearity. They are power, linear momentum and Hamiltonian. The conserved quantities are computed from their respective densities.

Under investigation in this paper is a discrete modified exponential Toda lattice equation which may describe vibration of particles in a lattice. Firstly, we construct an integrable lattice hierarchy associated with this equation from a $$2\times 2$$ matrix spectral problem, and some related integrable properties such as Hamiltonian structures, Liouville integrability and conservation laws of this hierarchy are discussed. Secondly, we present the discrete generalized $$(m, N-m)$$ -fold Darboux transformation of the modified exponential Toda lattice equation on the basis of its known Lax representation. As applications of the obtained discrete generalized Darboux transformation, multi-kink-soliton solutions on an exponential surface background and an inclined plane background are obtained when $$m=2N$$ , the discrete rational and semi-rational solutions are derived when $$m=1$$ , and the mixed solutions of usual soliton solutions and rational solutions are given when $$m=2$$ . Based on the asymptotic and graphic analysis, soliton elastic interaction phenomena and limit states related to rational solutions are discussed and analyzed. Furthermore, some mathematical features of rational solutions are summarized. Finally, numerical simulations are used to explore the dynamical behaviors of such soliton solutions which show the soliton evolutions are robust against a small noise. These results and properties given in this paper might be useful for understanding nonlinear lattice dynamics.

In recent few years, the Gauss-Bonnet f ( G , T ) theory of gravity has fascinated considerable researchers owing to its coupling of trace of the stress-energy tensor T with the Gauss-Bonnet term G . In this context, we focuss ourselves to study bouncing universe with in f ( G , T ) gravity background. Some important preliminaries are presented along with the discussion of cosmological parameters to develop a minimal background about f ( G , T ) theory of gravity. The exact bouncing solutions with physical analysis are provided with the choice of two equation of state parameters. It is shown that the results do agree with the present values of deceleration, jerk and snap parameters. Moreover, it is concluded that the model parameters are quite important for the validity of conservation equation (as the matter coupled theories do not obey the usual conservation law).

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establish the global existence of solutions and prove the $${C^{0,{1 \over 2}}}$$ -regularity of solutions near the degenerate boundary. We also compare the difference of solutions between the isothermal gas and the polytropic gas.

Under investigation in this paper is a semi-discrete modified KdV equation, which arises in a wide variety of fields, such as plasma physics, electromagnetic waves in ferromagnetic, antiferromagnetic or dielectric systems. With the help of the N − fold Darboux transformation and symbolic computation, the N − soliton solutions in determinant form are presented. Through the asymptotic and graphic analysis, the elastic interaction phenomena between or among two-, three- and four-soliton solutions are discussed in detail, and some important physical quantities are accurately analyzed. In addition, infinite number of conservation laws are also constructed to illustrate the integrability of the equation. The results in this paper might be helpful for understanding the propagation and interaction properties of electromagnetic waves.

We study small shocks of 1D scalar viscous conservation laws with uniformly convex flux and nonlinear dissipation. We show that such shocks are [Formula: see text] stable independently of the strength of the dissipation, even with large perturbations. The proof uses the relative entropy method with a spatially-inhomogeneous pseudo-norm.

Based on the zero-curvature equation and Lenard recursion equations, we propose a vector super long-wave-short-wave hierarchy associated with an ( n + 2 ) × ( n + 2 ) matrix spectral problem. A typical member in the hierarchy is the vector super Newell long-wave-short-wave equation. An infinite set of conservation laws for the vector super Newell long-wave-short-wave equation is constructed by using Liouville’s formula and the resulting super Riccati equation.

Electromagnetism is expressed from two basic postulates. They are light invarianceand charge conservation. At this work one extends the Maxwell scenario from macroscopic to microscopic electromagnetism by following the elementary particles electric charge microscopic behavior. It yields a triune electric charge interrelationship. Three charges {+, 0, −} be exchanged through a vector bosons quadruplet. It is called Four Bosons Electromagnetism. A systemic EM physics appears to be understood. Maxwell photon is not enough for describing the microscopic electric charge physics. An extension for electromagnetic energy is obtained. The fields quadruplet {Aµ, Uµ, Vµ±} are the porters of electromagnetic energy. They are the usual photon Aµ, massive photon Uµ and two charged photons Vµ±, A new understanding on EM phenomena has to be considered. A set determinism based on granular and collective fields is developed. A space-time evolution associated to a whole.Conservation laws are studied. The EM phenomena is enlarged to three charges interchanges to {+, 0, −}. Two novelties appear. New features on nonlinear fields acting as own sources and on electric charge physics. Properties as conservation, conduction, transmission, interaction are extended to a systemic electromagnetism. A whole conservation law for electric charge emerges from three charges interwoven. Electric charge has a systemic behavior. Although there is no Coulomb law for zero electric charge, the Four Bosons Electromagnetism contains an EM energy which provides a neutral electromagnetism. Particles with zero charge {Aµ, Uµ} are carrying EM energy. Another consideration is on EM energy being transported by four nonlinear fields. A new physicality appears. The abelian nonlinearity generates fields charges. Fields are working as own sources through mass terms, trilinear and quadrilinear interactions, spin couplings. Consequently the photon is more than being a consequence from electric charge oscillations. It is able to generate its own charge. Introduce the meaning of photonics.Thus, electric charge is no more the isolate electromagnetic source. There are another conservation laws. Fields sources appear through corresponding equations of motion, Bianchi identities, energy-momentum, Noether laws and angular momentum conservation laws. They move EM to a fields charges dependence. Together with electric charge they carrythe electromagnetic flux. Supporting the Ahranov-Bohm experiment of potential fields as primitive entities.

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law.

The concepts of Weak Values (WV) and Two-State Vector Formalism (TSVF) appear to motivate new experiments and to offer novel insights into dynamical processes in various materials of several scientific and technological fields. To support this view, here we consider the dynamics of hydrogen atoms and/or molecules in nanostructured materials like e.g., carbon nanotubes. The experimental method applied is incoherent scattering of thermal (i.e., non-relativistic) neutrons (INS). In short, the main finding consists in the following effect: the measured energy and momentum transfers are shown to contradict even qualitatively the associated expectations of conventional scattering theory. This effect was recently observed in INS experiments, e.g., in H2 adsorbed in carbon nanotubes, where a large momentum transfer deficit was found. Due to the broad abundance of hydrogen, these findings may be also of technological importance, since they indicate a considerably enhanced H mobility in specific structured material environments. A new INS experiment is proposed concerning the H mobility of an ultra-fast proton conductor (H3OSbTeO6) being of technological relevance. Further neutron scattering investigations on other systems (metallic hydrides and H2 encapsulated inside C60) are proposed. As concerns theoretical implications, the analysis of the experimental results strongly supports the view that the wavefunction (or state vector) represents an ontological physical entity of a single quantum system.

The paper shows that the Darwin-Breit form of electromagnetic interaction disproves the Aharonov-Bohm assertion about the fundamental meaning of the electromagnetic potentials in quantum theory. A specific analysis of the Aharonov-Bohm electric and magnetic effects substantiates this result.

Particle methods for high-viscous free-surface flows are of great use to capture flow behaviors which are intermediate between solid and liquid. In general, it is important for numerical methods to satisfy the fundamental laws of physics such as the conservation laws of mass and momentum and the thermodynamic laws. Especially, the angular momentum conservation is necessary to calculate rotational motion of high-viscous objects. However, most of the particle methods do not satisfy the physical laws in their spatially discretized system. The angular momentum conservation law is broken mostly because of the viscosity models, which may result in physically strange behavior when high-viscous free-surface flow is calculated. In this study, a physically consistent particle method for high-viscous free-surface flows is developed. The present method was verified, and its performance was shown with calculating flow in a rotating circular pipe, high-viscous Taylor–Couette flow, and offset collision of a high-viscous object.

The exact non-static accelerating solutions of Einstein field equations in non-comoving pure radiation fields, corresponding to an indefinite non-degenerate metric in cartesian coordinates, are obtained. The gravitational field is of Petrov type D and the considered spacetime is not conformally flat. Lie symmetry method is used for symmetry reduction of nonlinear partial differential equations and for finding the exact solutions, comprising both arbitrary functions and known analytic functions. Conservation laws are obtained by using multiplier approach. The graphical representations of solutions are shown by considering different possibilities of the arbitrary functions.

We derive conservation laws for so-called generalized nonlinear Schrodinger equation (GNLSE), which describes a propagation of super-short femtosecond pulse in a medium with cubic nonlinear response in the framework of slowly-evolving-wave approximation (SEWA). We take into account the beam diffraction, the pulse spreading due to second order dispersion, the pulse self-steepening, as well as mixed derivatives of the pulse envelope. Such nonlinear interaction of the laser pulse with a medium is widely investigated by many authors because various substances manifest a cubic nonlinear response of medium in various laser systems. However, until present time the conservation laws (integrals of motion) of the GNLSE are absent. For their deriving we propose a novel transform of the GNLSE. It results in an equation containing neither the derivative of a term describing the nonlinear response of medium nor mixed derivatives of a complex amplitude. In new variables, the femtosecond pulse propagation is described by three equations containing only the linear differential operators. Using this transform, the conservation laws for a problem under consideration are found out. We claim that for avoiding a non-physical modulation instability of a laser pulse propagation it is necessary to satisfy to a spectral invariant at the frequency, which is singular one in the Fourier space. This frequency is inherent to the GNLSE. The conservation laws allow developing the conservative finite-difference schemes that preserve difference analogs of these laws.

In the present paper, a new (3 + 1)-dimensional Schrodinger equation in Quantum Mechanics is derived. Based on the extended (3 + 1)-dimensional zero curvature equation, this equation is derived for the first time via the compatibility condition. Meanwhile, some soliton solutions are presented. Finally, conservation laws also obtained.

In this paper, the time-fractional coupled Burger equation under Riemann-Liouville derivative is systematically analyzed. Firstly, the Lie point symmetry is obtained by applying the Lie symmetry an...

In this study, lie symmetry analysis, conservation theorem and improved fractional sub-equation method are discussed. The given methods are applied to the time fractional Ito equation. Firstly, we ...

This paper obtains optical soliton solutions of the Kudryashov’s model with arbitrary refractive index. Three integration algorithms collectively revealed a full spectrum of single solitons along with a straddled soliton. The constraint conditions for the existence of such solitons are also listed. Finally, the only conserved quantity, supported by the model, is penned down.

This paper aims to study a ( $$3+1$$ )-dimensional novel KP-like equation, which arises in the analysis of versions of resonant phenomena. The classical symmetry approach will be employed to search for exact solutions. Thereafter, we will search for the admitted conserved vectors of the mentioned novel KP-like equation. Although Kuo and Ma (Wave Random Complex, https://doi.org/10.1080/17455030.2020.1792580 , 2020) have given a recommendable effort to solve a new ( $$3+1$$ )-dimensional novel KP-like equation, there is no unified method. The method employed in Kuo and Ma (Wave Random Complex, https://doi.org/10.1080/17455030.2020.1792580 , 2020), cannot be used to construct conservation laws or point symmetries and hence this prompted the utilization of the classical symmetry approach for the underlying equation.

Classical hydrodynamics is a remarkably versatile description of the coarse-grained behavior of many-particle systems once local equilibrium has been established. The form of the hydrodynamical equations is determined primarily by the conserved quantities present in a system. Some quantum spin chains are known to possess, even in the simplest cases, a greatly expanded set of conservation laws, and recent work suggests that these laws strongly modify collective spin dynamics even at high temperature. Here, by probing the dynamical exponent of the one-dimensional Heisenberg antiferromagnet KCuF$_3$ with neutron scattering, we find evidence that the spin dynamics are well described by the dynamical exponent $z=3/2$, which is consistent with the recent theoretical conjecture that the dynamics of this quantum system are described by the Kardar-Parisi-Zhang universality class. This observation shows that low-energy inelastic neutron scattering at moderate temperatures can reveal the details of emergent quantum fluid properties like those arising in non-Fermi liquids in higher dimensions., 12 pages and 4 figures. Includes 1 pages of methods and >> 1 pages Supplementary Information

The thermal management of a system needs an accurate and efficient measurement of exergy. For optimal performance, entropy should be minimized. This study explores the enhancement of the thermal exchange and entropy in the stream of Eyring–Powell fluid comprising nanoparticles saturating the vertical oriented dual cylindrical domain with uniform thermal conductivity and viscous dissipation effects. A symmetrical sine wave over the walls is used to induce the flow. The mathematical treatment for the conservation laws are described by a set of PDEs, which are, later on, converted to ordinary differential equations by homotopy deformations and then evaluated on the Mathematica software tool. The expression of the pressure rise term has been handled numerically by using numerical integration by Mathematica through the algorithm of the Newton–Cotes formula. The impact of the various factors on velocity, heat, entropy profile, and the Bejan number are elaborated pictorially and tabularly. The entropy generation is enhanced with the variation of viscous dissipation but reduced in the case of the concentration parameter, but viscous dissipation reveals opposite findings for the Newtonian fluid. From the abovementioned detailed discussion, it can be concluded that Eyring–Powell shows the difference in behavior in the entropy generation and in the presence of nanoparticles due to the significant dissipation effects, and also, it travels faster than the viscous fluid. A comparison between the Eyring-Powell and Newtonian fluid are also made for each pertinent parameter through special cases. This study may be applicable for cancer therapy in biomedicine by nanofluid characteristics in various drugs considered as a non-Newtonian fluid.

Methods for detecting Bose–Einstein condensate of light and dark excitons are considered. The features of the resulting radiation during the decay of condensate excitons are investigated. The recombination of these quasiparticles is studied, taking into account phase synchronism.

The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

An analysis based on the law of linear momentum conservation demonstrates unequivocally that the mass fraction is the scalar whose gradient determines gas diffusion, both molecular and turbulent. It illustrates sizeable errors in previous micrometeorological definitions of the turbulent gas flux based on fluctuations in other scalars such as the mixing ratio or density. In deference to conservation law, we put forth a new definition for the turbulent gas flux. Net gas transport is then defined as the sum of this turbulent flux with systematic transport by the mean flow. This latter, non-diffusive flux is due to the net upward boundary-layer momentum, a Stefan flow forced by evaporation, which is the dominant surface gas exchange. A comparison with the traditional methodology shows exact agreement between the two methods regarding the net flux, but with the novelty of partitioning gas transport according to distinct physical mechanisms. The non-diffusive flux is seen to be non-negligible in general, and to dominate turbulent transport under certain conditions, with broad implications for boundary-layer meteorology., Spanish Ministry of Economy project ELEMENTAL CGL2017-83538-C3-1-R, Andalusian government P18-RT-3629, European Commission

In this work, the mechanism for the formation of the delta shock wave is analyzed to deal with interaction of delta shock waves and contact discontinuities for a system of Keyfitz–Kranzer type by means of analysis and solutions of Riemann problems. A set of numerical experiments are provided, illustrating the theoretical findings numerically. A brief survey of the Keyfitz–Kranzer systems as a base model of fundamental nonlinear phenomena in applications is provided aiming to shed light on the intricate wave structure for other related models of conservation laws appearing in applied sciences.