Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics

Seadawy, Aly R.; Ahmed, S.; Rizvi, Syed T. R.; Ali, Kashif

doi:10.1016/j.geomphys.2022.104507

Cited by 37 publications

(4 citation statements)

References 53 publications

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“…However, m j (1 ≤ j ≤ 5) represents any constants. By using Equation (7) in Equation (6) and collecting the coefficients of ε, we then solve the system of equations to find the values of the parameters:…”

Section: Rational M-shaped Solution (Msrs)mentioning

confidence: 99%

“…Physics and engineering are two mathematics-based sciences that frequently use PDEs [1][2][3][4]. The fundamentals of contemporary scientific logic are formed by them for several ideas, including heat, sound, diffusion, electrodynamics [5][6][7], electrostatics, elastic, hydrodynamics, and quantum mechanics [8][9][10]. A wide range of scientific fields are interested in studying nonlinear wave phenomena [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

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We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots.

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Section: Rational M-shaped Solution (Msrs)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

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“…For instance, the Korteweg-de Vries equation governs shallow water wave dynamics near ocean shores and beaches, and the nonlinear Schrödinger's equation governs the propagation of solitons through optical fibers. Some examples of PDEs and their applications can be found in [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

2023

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This article studies diverse forms of lump-type solutions for coupled nonlinear generalized Zakharov equations (CNL-GZEs) in plasma physics through an appropriate transformation approach and bilinear equations. By utilizing the positive quadratic assumption in the bilinear equation, the lump-type solutions are derived. Similarly, by employing a single exponential transformation in the bilinear equation, the lump one-soliton solutions are derived. Furthermore, by choosing the double exponential ansatz in the bilinear equation, the lump two-soliton solutions are found. Interaction behaviors are observed and we also establish a few new solutions in various dimensions (3D and contour). Furthermore, we compute rogue-wave solutions and lump periodic solutions by employing proper hyperbolic and trigonometric functions.

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“…The exact solutions of integrable equations can give an vital assurance for the analysis of their different properties. Since the birth of soliton, several techniques for solving classical integrable equations have been studied [1][2][3][4][5][6]. As we all are familiar with NLSE and the derivative NLSE, which are significant equations in the field of mathematical physics, movement of microscopic particles, quantum mechanics, nonlinear optics and plasma physics [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Applications for mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation in water wave flumes and optical fibers

et al. 2022

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In this work, by applying the symbolic computation with ansatz functions approach and logarithmic transformation, we investigate the analytical rational solitons of the mixed Chen-Lee-Liu derivative nonlinear Schrödinger (MCLLNLS)-equation. We acquire two categories of M-shaped rational solutions and their dynamics are revealed in figures by choosing the proper vales of concerned parameters. Moreover two types of interaction of M-shaped rational solutions with kink wave are computed. Furthermore we evaluate multiwaves solutions, Homoclinic breather, kink cross-rational solutions and periodic cross-rational solutions for governing model. We also investigate the stability property of attained solutions and present in the form of table.

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Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics

Cited by 37 publications

References 53 publications

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

Applications for mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation in water wave flumes and optical fibers

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