The Weierstrass and Jacobi elliptic solutions along with multiwave, homoclinic breather, kink-periodic-cross rational and other solitary wave solutions to Fornberg Whitham equation

Bashir, Azhar; Seadawy, Aly R.; Ahmed, Sarfaraz; Rizvi, Syed T. R.

doi:10.1016/j.chaos.2022.112538

Cited by 27 publications

(4 citation statements)

References 46 publications

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“…where c is the non-zero velocity of the soliton, A(ψ) and B(ψ) are real functions explaining the appearance of the solitary wave. Inserting equation (5) and equation (35) in equation (1) we achieve a system of ODEs…”

Section: Sub-ode Techniquementioning

confidence: 99%

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Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Ali,

Seadawy,

Rizvi

et al. 2024

Commun. Theor. Phys.

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In this article, we explore the famous Selkov-Schnakenberg (SS) system of coupled nonlinear partial differential equations (PDEs) for Lie symmetry analysis (LSA), Self Adjointness (SA) and Conservation laws (CLs). Moreover miscellaneous soliton solutions like dark, bright, periodic, rational, Jacobian elliptic function (JEF), Weierstrass elliptic and hyperbolic solutions of SS system will be achieved by a well-known technique called Sub-ODE. All these results are displayed graphically by 3D, 2D and contour plots.

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Section: Sub-ode Techniquementioning

confidence: 99%

“…A soliton is a wave that retains its shape and velocity on collision with another soliton. Many researchers have worked on finding the soliton solutions of the models [34][35][36][37][38][39][40] by different techniques.…”

Section: Introductionmentioning

confidence: 99%

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Ali,

Seadawy,

Rizvi

et al. 2024

Commun. Theor. Phys.

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“…Using Equation (), multi‐waves method, homoclinic breather approach, and interactional solution with double

\mathit{\exp}

‐functions strategy are discussed [55–60].…”

Section: Cubic Law Nonlinearity and The Fractional‐order Complex Tran...mentioning

confidence: 99%

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Kopçasız,

Yaşar

2023

Math Methods in App Sciences

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This work concerns the fractional‐order dual‐mode nonlinear Schrödinger equation (FDMNLSE), which portrays the augmentation or absorption of dual waves. This model dissects the concurrent generation of two characteristic waves dealing with dual modes and introduces three physical parameters: nonlinearity, phase velocity, and dispersive factor. In the context of photonics, NLSE models the propagation of soliton pulses over intercontinental distances. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. We analyze the multi‐waves method, homoclinic breather approach, and interactional solution with the double ‐functions procedure, and their applications for this equation are obtained using logarithmic transformation. The multi‐wave method is a well‐known phenomenon in nonlinear science that describes the interaction of three waves that satisfy certain resonance conditions. A breather wave is a localized and oscillatory solution that maintains its shape over time. Finally, we will discuss the dynamics of our newly obtained solutions with the help of graphs by assigning appropriate values to the parameters. The proposed methods are straight and aggressive, so the approved form can be extended for more nonlinear models. The findings are exceptional in comparison to previous findings in the literature. These outcomes may have significance for additional investigation of such frameworks to handle the nonlinear issues in applied sciences. The obtained results help us understand fluid propagation and incompressible fluids.

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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

Self Cite

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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 Weierstrass and Jacobi elliptic solutions along with multiwave, homoclinic breather, kink-periodic-cross rational and other solitary wave solutions to Fornberg Whitham equation

Cited by 27 publications

References 46 publications

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

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

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