New soliton solutions of Simplified Modified Camassa Holm equation, Klein–Gordon–Zakharov equation using First Integral Method and Exponential Function Method

Javeed, Shumaila; Abbasi, Muhammad Awais; Imran, Tayyab; Fayyaz, Rabia; Ahmad, Harith; Botmart, Thongchai

doi:10.1016/j.rinp.2022.105506

Cited by 6 publications

(1 citation statement)

References 38 publications

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“…Diverse researchers have examined analytical solitary wave solutions to some significant NLEEs in applied mathematics by executing the first integral approach; videlicet, Akbar et al [27] applied the first integral approach to obtain the analytical solutions to the Chaffee-Infante equation and the Zakharov equation. To gain the analytical solutions to the Klein-Gordon-Zakharov equation and the simplified modified Camassa Holm equation, Javeed et al [28] used this technique. The technique was also used to attain detailed solutions to the Riemann wave equation [29].…”

Section: Introductionmentioning

confidence: 99%

Analytic soliton solutions to the shallow water dispersive long gravity wave equations: the first integral approach in nonlinear physics

Hussain,

Akbar,

İlhan

2024

Phys. Scr.

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In this article, we investigate the (2+1)-dimensional dispersive long water wave equation and the (1+1)-dimensional PHI-four equation, which describe the behavior of long gravity waves with small amplitudes, long wave propagation in oceans and seas, coastal structures and harbor design, effects of wave motion on sediment transport, quantum field theory, phase transitions of matter, ferromagnetic systems, liquid-gas transitions, and the structure of optical solitons. We use the first integral technique and obtain new and generic solutions for the models under consideration. By setting definite values for the associated parameters, various types of richly structured solitons are generated. The solitons include kink, flat kink, bell-shaped, anti-bell-shaped, and singular kink formations. These solutions allow for a profound understanding of the behavior and properties of the phenomena, offering new insights and potential applications in the associated field. The first integral technique is simpler, directly integrates the models, and the solutions offer clear insights into the underlying phenomena without requiring intermediate steps, making it widely applicable to various other models, including nonlinear equations and those that are challenging to solve using other standard techniques.

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Section: Introductionmentioning

confidence: 99%

Analytic soliton solutions to the shallow water dispersive long gravity wave equations: the first integral approach in nonlinear physics

Hussain,

Akbar,

İlhan

2024

Phys. Scr.

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Simulations of exact explicit solutions of simplified modified form of Camassa–Holm equation

Akram,

Sadaf,

Arshed

et al. 2024

Opt Quant Electron

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Novel Approaches to Fractional Klein–gordon–zakharov Equation

WANG

2023

Fractals

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The Klein–Gordon–Zakharov equation is an important and interesting model in physics. A fractional Klein–Gordon–Zakharov model is described by employing beta-derivative. Some new solitary wave solutions are acquired by utilizing the fractional rational [Formula: see text]–[Formula: see text] method and fractional [Formula: see text] method. Some 3D graphs are depicted to elaborate these new solitary wave solutions. The work is very helpful to study other related types of fractional evolution equations.

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New soliton solutions of Simplified Modified Camassa Holm equation, Klein–Gordon–Zakharov equation using First Integral Method and Exponential Function Method

Cited by 6 publications

References 38 publications

Analytic soliton solutions to the shallow water dispersive long gravity wave equations: the first integral approach in nonlinear physics

Analytic soliton solutions to the shallow water dispersive long gravity wave equations: the first integral approach in nonlinear physics

Simulations of exact explicit solutions of simplified modified form of Camassa–Holm equation

Novel Approaches to Fractional Klein–gordon–zakharov Equation

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