Solitary waves of the generalized Zakharov equations via integration algorithms

Hammad Alotaibi; Hammad Alotaibi

doi:10.3934/math.2024619

AIMS Mathematics

2024, Volume 9, Issue 5: 12650-12677. doi: 10.3934/math.2024619

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Solitary waves of the generalized Zakharov equations via integration algorithms

Hammad Alotaibi ^,

Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 19 November 2023 Revised: 03 February 2024 Accepted: 07 February 2024 Published: 02 April 2024
MSC : 11T71

In many applications, the investigation of traveling wave solutions is essential in obtaining an accurate description of the dynamical behavior of most physical phenomena. The exact solutions to nonlinear equations can provide more physical descriptions and insightful details for many problems of practical interest. This paper focuses on investigating the solitary wave solutions of the generalized Zakharov equations (GZEs) by using four integration algorithms, namely, the modified $ (g'/g^{2}) $-expansion method, the modified $ (g') $-expansion method, the generalized simple ($ w/g $)-expansion method, and the addendum to Kudryashov's method. The GZEs have been widely used to describe the propagation of Langmuir waves in the field of plasma physics. The efficiency and simplicity of these methods are evaluated based on their application to GZEs, which have yielded multiple new optical solitary wave solutions in the form of rational, trigonometric, and hyperbolic functions. By using a suitable wave transformation, the coupled nonlinear partial differential equations are converted into ordinary differential equations. The derived optical solutions are graphically depicted in $ 2 $D and $ 3 $D plots for some specific parameter values. The traveling wave solutions discovered in the current study constitute just one example of the desired solutions that may enable the exploration of the physical properties of many complex systems and could also contribute greatly to improving our understanding of many interesting natural phenomena that arise in different applications, including plasma physics, fluid mechanics, protein chemistry, wave propagation, and optical fibers.
- solitary solutions,
- integration algorithms,
- fluid dynamics,
- physical phenomena,
- generalized Zakharov equations
Citation: Hammad Alotaibi. Solitary waves of the generalized Zakharov equations via integration algorithms[J]. AIMS Mathematics, 2024, 9(5): 12650-12677. doi: 10.3934/math.2024619

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Abstract

In many applications, the investigation of traveling wave solutions is essential in obtaining an accurate description of the dynamical behavior of most physical phenomena. The exact solutions to nonlinear equations can provide more physical descriptions and insightful details for many problems of practical interest. This paper focuses on investigating the solitary wave solutions of the generalized Zakharov equations (GZEs) by using four integration algorithms, namely, the modified $ (g'/g^{2}) $-expansion method, the modified $ (g') $-expansion method, the generalized simple ($ w/g $)-expansion method, and the addendum to Kudryashov's method. The GZEs have been widely used to describe the propagation of Langmuir waves in the field of plasma physics. The efficiency and simplicity of these methods are evaluated based on their application to GZEs, which have yielded multiple new optical solitary wave solutions in the form of rational, trigonometric, and hyperbolic functions. By using a suitable wave transformation, the coupled nonlinear partial differential equations are converted into ordinary differential equations. The derived optical solutions are graphically depicted in $ 2 $D and $ 3 $D plots for some specific parameter values. The traveling wave solutions discovered in the current study constitute just one example of the desired solutions that may enable the exploration of the physical properties of many complex systems and could also contribute greatly to improving our understanding of many interesting natural phenomena that arise in different applications, including plasma physics, fluid mechanics, protein chemistry, wave propagation, and optical fibers.

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