Fundamental Solutions for the Coupled KdV System and Its Stability

Abdelrahman, Mahmoud A. E.; Almatrafi, M. B.; Alharbi, Abdulghani

doi:10.3390/sym12030429

Cited by 24 publications

(5 citation statements)

References 43 publications

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“…The important features of new solitonic envelopes form a foundation for the novel scientific energy universe, which is of great importance for a number of disciplines, including plasma physics, solid-state physics, telecommunications, superfluidity, quantum mechanics, and astrophysical dynamics [1][2][3][4][5][6]. These types of solution have attracted particular attention from physicists, mathematicians, and engineers [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation

et al. 2023

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The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines the energy characteristics of quantum physics’ fractional Hall effect edge states. The sine-Gordon expansion technique (SGET) was implemented to extract stochastic solutions for the CNLSE through multiplicative noise effects. This method accurately described a variety of solitary behaviors, including bright solitons, dark periodic envelopes, solitonic forms, and dissipative and dissipative–soliton-like waves, showing how the solutions changed as the values of the studied system’s physical parameters were changed. The stochastic parameter was shown to affect the damping, growth, and conversion effects on the bright (dark) envelope and shock-forced oscillatory wave energy, amplitudes, and frequencies. In addition, the intensity of noise resulted in enormous periodic envelope stochastic structures and shock-forced oscillatory behaviors. The proposed technique is applicable to various energy equations in the nonlinear applied sciences.

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Section: Introductionmentioning

confidence: 99%

Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation

et al. 2023

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“…As a result, some researchers have revealed numerous effective methods. Some of the powerful approaches are the Sine-Gordon expansion approach [1], the modified simple equation technique [2], the tanh-sech process [3,4], the trial equation method [5], the exp(−f (ζ ))-expansion principal [6,7] and the generalized exponential rational function approach [8]. More methods can be easily seen in references [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A Study of Traveling Wave Structures and Numerical Investigation of Two-Dimensional Riemann Problems with Their Stability and Accuracy

Alharbi¹

2023

Computer Modeling in Engineering &Amp; Sciences

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The Riemann wave system has a fundamental role in describing waves in various nonlinear natural phenomena, for instance, tsunamis in the oceans. This paper focuses on executing the generalized exponential rational function approach and some numerical methods to obtain a distinct range of traveling wave structures and numerical results of the two-dimensional Riemann problems. The stability of obtained traveling wave solutions is analyzed by satisfying the constraint conditions of the Hamiltonian system. Numerical simulations are investigated via the finite difference method to verify the accuracy of the obtained results. To extract the approximation solutions to the underlying problem, some ODE solvers in FORTRAN software are applied, and outcomes are shown graphically. The stability and accuracy of the numerical schemes using Fourier's stability method and error analysis, respectively, to increase the reassurance are investigated. A comparison between the analytical and numerical results is obtained and graphically provided. The proposed methods are effective and practical to be applied for solving more partial differential equations (PDEs).

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“…Investigation of optical solutions has distinctly acquired momentum in the field of the solitary waves. [1][2][3][4][5] In dielectric fibers, the dynamic balance between the optical Kerr effect and dispersion generates an optical solution. Indeed, solutions have acquired much attention because of their robust nature and powerful applications in all long-distance and optical communications.…”

Section: Introductionmentioning

confidence: 99%

Some new chiral and perturbed chiral solitary waves in quantum Hall effect

Al-Saleh,

Hassan,

Alomair

et al. 2023

Journal of Algorithms & Computational Technology

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In this article, we present a new form of solutions to the Chiral/perturbed Chiral nonlinear Schrödinger equation, using the unified solver method. This solver introduces the closed formula in an explicit way. In each problem, different families of elliptic functions solutions are found under suitable conditions. Moreover, some cases of hyperbolic solutions are obtained. The acquired solutions may be applicable for explaining various complex phenomena in the quantum Hall effect. The presented study displays that the proposed solver is simple, powerful and sturdy. For more details about the physical dynamical representation of the presented solutions, we introduce some graphs of some selected solutions using Matlab software. Finally, the presented solver can be used to solve many other models in real life problems.

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Fundamental Solutions for the Coupled KdV System and Its Stability

Cited by 24 publications

References 43 publications

Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation

Characteristics of New Stochastic Solitonic Solutions for the Chiral Type of Nonlinear Schrödinger Equation

A Study of Traveling Wave Structures and Numerical Investigation of Two-Dimensional Riemann Problems with Their Stability and Accuracy

Some new chiral and perturbed chiral solitary waves in quantum Hall effect

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