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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Nonlinear Dispersion Dynamics of Optical Solitons of Zoomeron Equation with New $varphi ^{6}$-Model Expansion Approach

Journal of Vibration Testing and System Dynamics 8(3) (2024) 285--307 | DOI:10.5890/JVTSD.2024.09.002

Muhammad Abubakar Isah$^1$, Asif Yokus$^{1,2}$

$^{1}$ Firat University, Faculty of Science, Department of Mathematics, Elazig, Turkey

$^{2}$ Application and Research Center Advisory Board Member, Istanbul Commerce University, Istanbul, Turkey

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Abstract

One of the equations describing incognito evolution, the nonlinear Zoomeron equation, is studied in this work. In a variety of physical circumstances, including laser physics, fluid dynamics and nonlinear optics, solitons with particular properties arise and the Zoomeron equation is a single example of one such situation. The method of $\varphi^6$-model expansion allows for the explicit retrieval of a wide range of solution types, including kink-type solitons, these solitons are also called topological solitons in the context of water waves, their velocities do not depend on the wave amplitude, others are bright, singular, periodic and combined singular soliton solutions. The outcomes of this research may improve the Zoomeron equation's nonlinear dynamical features. The method proposes a practical and effective approach for solving a large class of nonlinear partial differential equations. The nonlinear dispersion behavior is analyzed for different values of the magnitude, which physically represents the wave velocity, from the parameters of the generated traveling wave solutions. Interesting graphs are employed to explain and highlight the dynamical aspects of the results, and all of the obtained results are put into the Zoomeron equation to show the accuracy of the results.

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