13 results on '"Faridi, Waqas Ali"'
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2. Optical solitonic structures with singular and non-singular kernel for nonlinear fractional model in quantum mechanics
- Author
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Asjad, Muhammad Imran, Inc, Mustafa, Faridi, Waqas Ali, Bakar, Muhammad Abu, Muhammad, Taseer, and Rezazadeh, Hadi
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- 2023
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3. Dynamical study of optical soliton structure to the nonlinear Landau–Ginzburg–Higgs equation through computational simulation.
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Iqbal, Mujahid, Faridi, Waqas Ali, Ali, Rashid, Seadawy, Aly R., Rajhi, Ali A., Anqi, Ali E., Duhduh, Alaauldeen A., and Alamri, Sagr
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NONLINEAR equations , *SOLITONS , *NONLINEAR waves , *THEORY of wave motion , *OPTICAL engineering , *OCEAN engineering , *NONLINEAR Schrodinger equation , *MODE-locked lasers - Abstract
In this research work, the nonlinear Landau–Ginzburg–Higgs model under investigation on the base of auxiliary equation method. The nonlinear Landau–Ginzburg–Higgs equation mainly describe nonlinear wave propagation, categorizes wave velocity, and materializes several phenomena through the dispersive system. The secured optical soliton solutions are interested, more general and some novel in kink solitons, bright solitons, periodic singular solitons, anti-kink solitons and dark solitons. The physical structure of some explored solitons solutions are represented graphically as contour, 2D and 3D plots by utilizing the symbolic computational tool Mathematica. The secured soliton will be play important role to the investigation of nonlinear phenomena in the various domains of nonlinear sciences and engineering such as optical fibers, nonlinear dynamics, communication system, solitons wave theory, nonlinear optics, transmission system, electronic engineering and ocean engineering. The auxiliary equation method is a basic analytical, powerful, efficient approach for the investigation of optical soliton inside the nonlinear Landau–Ginzburg–Higgs equation and also other nonlinear equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. Dynamical analysis of optical soliton structures for wave propagation in nonlinear low-pass electrical transmission lines under effective approach.
- Author
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Iqbal, Mujahid, Faridi, Waqas Ali, Alammari, Maha, Alomari, Faizah A. H., Alsubaie, Nahaa E., Ibrahim, Salisu, and Seadawy, Aly R.
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ELECTRIC lines , *NONLINEAR waves , *THEORY of wave motion , *MODE-locked lasers , *OPTICAL solitons , *SOLITONS , *NONLINEAR optics , *PHYSICAL sciences - Abstract
In this research work, we extracted the variety of newly optical soliton solutions which describe the wave propagation in nonlinear low-pass electrical transmission lines model by utilizing the auxiliary equation method. The secured solitons solutions yield a variety of typical soliton shapes, including dark solitons, periodic singular optical solitons, combined bright and dark solitons, kink wave solitons, bright solitons, ant-kink wave solitons, and solitary waves. The physical structure of extracted soliton solutions visualized in three different graphically structures such as three-dimension, two-dimensional and contour plotting on the choices of some constant parameters by utilizing the numerical simulations. This study explored optical solitons, solitary wave solutions, exact solitons for improving the performance of nonlinear low-pass electrical transmission systems. It provides an overview of solitons, their relevance, and stability principles. It also presents the mathematical formulation of the nonlinear low-pass electrical transmission lines model and discusses its implications for signal propagation. The secured soliton solutions have many applications in engineering and science such as nonlinear optics, fiber optics, laser optics, nonlinear dynamics, ocean engineering, electronic engineering, electrical engineering, computing engineering, power engineering and several other different kinds of physical sciences. The whole study shows that the suggested method is more powerful, effective, simple, and strong for looking into different types of nonlinear models involve in nonlinear sciences and the engineering presentation field. [ABSTRACT FROM AUTHOR]
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- 2024
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5. The fractional soliton solutions of dynamical system arising in plasma physics: The comparative analysis.
- Author
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Faridi, Waqas Ali, Iqbal, Mujahid, Riaz, Muhammad Bilal, AlQahtani, Salman A., and Wazwaz, Abdul-Majid
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PLASMA physics ,PLASMA Langmuir waves ,SOLITONS ,HAMILTON'S equations ,SCHRODINGER equation ,DYNAMICAL systems ,THEORY of wave motion ,ION acoustic waves - Abstract
In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions. [ABSTRACT FROM AUTHOR]
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- 2024
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6. On optical soliton wave solutions of non-linear Kairat-X equation via new extended direct algebraic method.
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Tipu, Ghulam Hussain, Faridi, Waqas Ali, Myrzakulova, Zhaidary, Myrzakulov, Ratbay, AlQahtani, Salman A., AlQahtani, Nouf F., and Pathak, Pranavkumar
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NONLINEAR equations , *GROUP velocity dispersion , *NONLINEAR waves , *SOLITONS , *OPTICAL solitons , *QUANTUM theory , *RICCATI equation - Abstract
The optical soliton is a hot topic in studying. In the current research, we utilize the modified extended direct algebraic method to derive optical soliton solutions for the non-linear Kairat-X (K-X) equation, which considers second-order spatiotemporal dispersion and the group velocity dispersion. The significant Kairat-X equation is considered to develop the soliton solutions because, Solitons are valuable because they are stable, retain their shape during propagation, and have applications ranging from telecommunications and signal processing to quantum physics and materials science. This equation describe how optical solitons propagate through non-linear media. Prior to this study, there was no existing research in which such solutions could be found. Our research yields various types of soliton solutions, including bright, dark, and singular solitons, as well as periodic and exponential solutions. Under specific parameters, we generate 2D, 3D, and contour graphs to visualize the propagation of optical soliton, allowing us to showcase its precise representation of physical phenomena. This work contributes to the advancement of our understanding of optical solitons and their behavior in non-linear optical systems. [ABSTRACT FROM AUTHOR]
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- 2024
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7. Formation of optical soliton wave profiles of Shynaray-IIA equation via two improved techniques: a comparative study.
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Faridi, Waqas Ali, Tipu, Ghulam Hussain, Myrzakulova, Zhaidary, Myrzakulov, Ratbay, and Akinyemi, Lanre
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MATHEMATICAL symmetry , *ALGEBRAIC equations , *SOLITONS , *TSUNAMIS , *PARTIAL differential equations , *EQUATIONS - Abstract
This study employs the new extended direct algebraic method and improved sardar sub-equation method to investigate solitary wave solutions in the Shynaray-IIA equation, which characterizes phenomena like tidal waves and tsunamis. These methods transform complex nonlinear coupled partial differential equations into manageable algebraic equations using a traveling wave transformation. Before this study, there is not exiting any research in which someone has obtained such kind of solutions. The main goal is to enhance understanding of the Shynaray-IIA equation behavior in various scenarios. By applying the new extended direct algebraic method and improved sardar sub-equation method, the study derives solitary wave solutions using trigonometric, hyperbolic, and Jacobi functions. By adjusting specific parameters, diverse solutions are obtained, including periodic, bell-shaped, anti-bell-shaped, M-shaped, and W-shaped solitons, each pair exhibiting mathematical symmetry. The analytical soliton solutions are further visualized in both 2D and 3D representations using Mathematica 12.3, aiding in the interpretation of these complex wave phenomena. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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8. The Sensitive Visualization and Generalized Fractional Solitons' Construction for Regularized Long-Wave Governing Model.
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Ur Rahman, Riaz, Faridi, Waqas Ali, El-Rahman, Magda Abd, Taishiyeva, Aigul, Myrzakulov, Ratbay, and Az-Zo'bi, Emad Ahmad
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PARTIAL differential equations , *ORDINARY differential equations , *FRACTIONAL differential equations , *CAPUTO fractional derivatives , *SOLITONS , *VISUALIZATION , *LAPLACIAN operator , *MATHEMATICAL regularization - Abstract
The solution of partial differential equations has generally been one of the most-vital mathematical tools for describing physical phenomena in the different scientific disciplines. The previous studies performed with the classical derivative on this model cannot express the propagating behavior at heavy infinite tails. In order to address this problem, this study addressed the fractional regularized long-wave Burgers problem by using two different fractional operators, Beta and M-truncated, which are capable of predicting the behavior where the classical derivative is unable to show dynamical characteristics. This fractional equation is first transformed into an ordinary differential equation using the fractional traveling wave transformation. A new auxiliary equation approach was employed in order to discover new soliton solutions. As a result, bright, periodic, singular, mixed periodic, rational, combined dark–bright, and dark soliton solutions were found based on the constraint relation imposed on the auxiliary equation parameters. The graphical visualization of the obtained results is displayed by taking the suitable parametric values and predicting that the fractional order parameter is responsible for controlling the behavior of propagating solitary waves and also providing the comparison between fractional operators and the classical derivative. We are confident about the vital applications of this study in many scientific fields. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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9. Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration.
- Author
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Majid, Sheikh Zain, Faridi, Waqas Ali, Asjad, Muhammad Imran, Abd El-Rahman, Magda, and Eldin, Sayed M.
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WAVE equation , *SOLITONS , *NONLINEAR wave equations , *MATHEMATICAL physics , *OCEAN waves , *TSUNAMIS , *WAVENUMBER - Abstract
The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics. [ABSTRACT FROM AUTHOR]
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- 2023
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10. The Propagating Exact Solitary Waves Formation of Generalized Calogero–Bogoyavlenskii–Schiff Equation with Robust Computational Approaches.
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Al Alwan, Basem, Abu Bakar, Muhammad, Faridi, Waqas Ali, Turcu, Antoniu-Claudiu, Akgül, Ali, and Sallah, Mohammed
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NONLINEAR differential equations ,ORDINARY differential equations ,THREE-dimensional imaging ,TRAVELING waves (Physics) ,PARTIAL differential equations ,SOLITONS ,WAVENUMBER ,NONLINEAR evolution equations ,DARBOUX transformations - Abstract
The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero–Bogoyavlenskii–Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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11. New Explicit Propagating Solitary Waves Formation and Sensitive Visualization of the Dynamical System.
- Author
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Zulqarnain, Rana Muhammad, Ma, Wen-Xiu, Eldin, Sayed M., Mehdi, Khush Bukht, and Faridi, Waqas Ali
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DYNAMICAL systems ,NONLINEAR Schrodinger equation ,ELLIPTIC functions ,VISUALIZATION ,SOLITONS - Abstract
This work discusses the soliton solutions for the fractional complex Ginzburg–Landau equation in Kerr law media. It is a particularly fascinating model in this context as it is a dissipative variant of the Hamiltonian nonlinear Schrödinger equation with solutions that create localized singularities in finite time. The ϕ 6 -model technique is one of the generalized methodologies exerted on the fractional complex Ginzburg–Landau equation to find the new solitary wave profiles. As a result, solitonic wave patterns develop, including Jacobi elliptic function, periodic, dark, bright, single, dark-bright, exponential, trigonometric, and rational solitonic structures, among others. The assurance of the practicality of the solitary wave results is provided by the constraint condition corresponding to each achieved solution. The graphical 3D and contour depiction of the attained outcomes is shown to define the pulse propagation behaviors while imagining the pertinent data for the involved parameters. The sensitive analysis predicts the dependence of the considered model on initial conditions. It is a reliable and efficient technique used to generate generalized solitonic wave profiles with diverse soliton families. Furthermore, we ensure that all results are innovative and mark remarkable impacts on the prevailing solitary wave theory literature. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
12. The First Integral of the Dissipative Nonlinear Schrödinger Equation with Nucci's Direct Method and Explicit Wave Profile Formation.
- Author
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Abu Bakar, Muhammad, Owyed, Saud, Faridi, Waqas Ali, Abd El-Rahman, Magda, and Sallah, Mohammed
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NONLINEAR Schrodinger equation ,PLASMA physics ,PARTIAL differential equations ,ATOMIC physics ,SOLITONS ,WAVENUMBER ,INTEGRALS - Abstract
The propagation of optical soliton profiles in plasma physics and atomic structures is represented by the (1 + 1) − dimensional Schrödinger dynamical equation, which is the subject of this study. New solitary wave profiles are discovered by using Nucci's scheme and a new extended direct algebraic method. The new extended direct algebraic approach provides an easy and general mechanism for covering 37 solitonic wave solutions, which roughly corresponds to all soliton families, and Nucci's direct reduction method is used to develop the first integral and the exact solution of partial differential equations. Thus, there are several new solitonic wave patterns that are obtained, including a plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, a mixed trigonometric solution, a trigonometric solution, a shock solution, a mixed shock singular solution, a mixed singular solution, a complex solitary shock solution, a singular solution, and shock wave solutions. The first integral of the considered model and the exact solution are obtained by utilizing Nucci's scheme. We present 2-D, 3-D, and contour graphics of the results obtained to illustrate the pulse propagation characteristics while taking suitable values for the parameters involved, and we observed the influence of parameters on solitary waves. It is noticed that the wave number α and the soliton speed μ are responsible for controlling the amplitude and periodicity of the propagating wave solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
13. The Enhancement of Energy-Carrying Capacity in Liquid with Gas Bubbles, in Terms of Solitons.
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Asghar, Umair, Faridi, Waqas Ali, Asjad, Muhammad Imran, and Eldin, Sayed M.
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LIQUEFIED gases , *NONLINEAR evolution equations , *ORDINARY differential equations , *SOLITONS , *BUBBLES , *PLASMA physics - Abstract
A generalized (3 + 1)-dimensional nonlinear wave is investigated, which defines many nonlinear phenomena in liquid containing gas bubbles. Basic theories of the natural phenomenons are usually described by nonlinear evolution equations, for example, nonlinear sciences, marine engineering, fluid dynamics, scientific applications, and ocean plasma physics. The new extended algebraic method is applied to solve the model under consideration. Furthermore, the nonlinear model is converted into an ordinary differential equation through the next wave transformation. A well-known analytical approach is used to obtain more general solutions of different types with the help of Mathematica. Shock, singular, mixed-complex solitary-shock, mixed-singular, mixed-shock singular, mixed trigonometric, periodic, mixed-periodic, mixed-hyperbolic solutions are obtained. As a result, it is found that the energy-carrying capacity of liquid with gas bubbles and its propagation can be increased. The stability of the considered model is ensured by the modulation instability gain spectrum generated and proposed with acceptable constant values. Two-dimensional, three-dimensional, and contour surfaces are plotted to see the physical properties of the obtained solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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