Exploring solitonic wave dynamics in the context of nonlinear conformable Kairat-X equation via unified method

Jamshad Ahmad; Zulaikha Mustafa; Mehjabeen Anwar; Marouan Kouki; Nehad Ali Shah; Jamshad Ahmad; Zulaikha Mustafa; Mehjabeen Anwar; Marouan Kouki; Nehad Ali Shah

doi:10.3934/math.2025495

AIMS Mathematics

2025, Volume 10, Issue 5: 10898-10916. doi: 10.3934/math.2025495

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Exploring solitonic wave dynamics in the context of nonlinear conformable Kairat-X equation via unified method

1.
Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat 50700, Pakistan; zulaikhamustafa11@gmail.com, mehjabeenanwar4@gmail.com
2.
Department of Information System, Faculty of Computing and Information Technology, Northern Border University, Rafha 76316, Saudi Arabia
3.
Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea; nehadali199@yahoo.com

Received: 04 March 2025 Revised: 18 April 2025 Accepted: 21 April 2025 Published: 13 May 2025
MSC : 35R11, 35B30, 35C07

This research is aimed at finding exact soliton solutions of the nonlinear fractional Kairat-X equation, which describes soliton behavior in nonlinear media and has applications in quantum physics, materials science, signal processing, and telecommunications. We use a unified method that generalizes the tanh-function method to find new exact soliton solutions in trigonometric, hyperbolic, and plane wave forms. Computational simulations with fixed parameters are performed to produce two-dimensional and three-dimensional visualizations, e.g., contour and density plots, representing the physical properties of the derived solitons. The simulations result in the identification of several soliton types, namely kink wave solitons, dark solitons, bright solitons, and periodic wave solitons. Our results increase the knowledge of the solution properties of the Kairat-X equation and give a platform to interpret a variety of significant physical phenomena. The systematicity and stability of our methodology prove its usefulness as a device for solving other nonlinear partial differential equations in applied physics and mathematics, always returning different exact solutions.
- the unified method,
- nonlinear conformable Kairat-X equation,
- exact solutions,
- bright solitons
Citation: Jamshad Ahmad, Zulaikha Mustafa, Mehjabeen Anwar, Marouan Kouki, Nehad Ali Shah. Exploring solitonic wave dynamics in the context of nonlinear conformable Kairat-X equation via unified method[J]. AIMS Mathematics, 2025, 10(5): 10898-10916. doi: 10.3934/math.2025495

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Abstract

This research is aimed at finding exact soliton solutions of the nonlinear fractional Kairat-X equation, which describes soliton behavior in nonlinear media and has applications in quantum physics, materials science, signal processing, and telecommunications. We use a unified method that generalizes the tanh-function method to find new exact soliton solutions in trigonometric, hyperbolic, and plane wave forms. Computational simulations with fixed parameters are performed to produce two-dimensional and three-dimensional visualizations, e.g., contour and density plots, representing the physical properties of the derived solitons. The simulations result in the identification of several soliton types, namely kink wave solitons, dark solitons, bright solitons, and periodic wave solitons. Our results increase the knowledge of the solution properties of the Kairat-X equation and give a platform to interpret a variety of significant physical phenomena. The systematicity and stability of our methodology prove its usefulness as a device for solving other nonlinear partial differential equations in applied physics and mathematics, always returning different exact solutions.

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