Lump and kink soliton phenomena of Vakhnenko equation

Khudhayr A. Rashedi; Saima Noor; Tariq S. Alshammari; Imran Khan; Khudhayr A. Rashedi; Saima Noor; Tariq S. Alshammari; Imran Khan

doi:10.3934/math.20241024

AIMS Mathematics

2024, Volume 9, Issue 8: 21079-21093. doi: 10.3934/math.20241024

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Lump and kink soliton phenomena of Vakhnenko equation

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55425, Saudi Arabia
2.
Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
4.
Department of Mathematics and Statistics, Bacha Khan University Charsadda, Pakistan

Received: 10 May 2024 Revised: 20 June 2024 Accepted: 24 June 2024 Published: 01 July 2024
MSC : 34G20, 35A20, 35A22, 35R11

Understanding natural processes often involves intricate nonlinear dynamics. Nonlinear evolution equations are crucial for examining the behavior and possible solutions of specific nonlinear systems. The Vakhnenko equation is a typical example, considering that this equation demonstrates kink and lump soliton solutions. These solitons are possible waves with several intriguing features and have been characterized in other naturalistic nonlinear systems. The solution of nonlinear equations demands advanced analytical techniques. This work ultimately sought to find and study the kink and lump soliton solutions using the Riccati–Bernoulli sub-ode method for the Vakhnenko equation (VE). The results obtained in this work are lump and kink soliton solutions presented in hyperbolic trigonometric and rational functions. This work reveals the effectiveness and future of our method for solving complex solitary wave problems.
- Lump and kink soliton,
- Vakhnenko equation,
- solitary waves,
- Riccati–Bernoulli sub-ode method
Citation: Khudhayr A. Rashedi, Saima Noor, Tariq S. Alshammari, Imran Khan. Lump and kink soliton phenomena of Vakhnenko equation[J]. AIMS Mathematics, 2024, 9(8): 21079-21093. doi: 10.3934/math.20241024

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Abstract

Understanding natural processes often involves intricate nonlinear dynamics. Nonlinear evolution equations are crucial for examining the behavior and possible solutions of specific nonlinear systems. The Vakhnenko equation is a typical example, considering that this equation demonstrates kink and lump soliton solutions. These solitons are possible waves with several intriguing features and have been characterized in other naturalistic nonlinear systems. The solution of nonlinear equations demands advanced analytical techniques. This work ultimately sought to find and study the kink and lump soliton solutions using the Riccati–Bernoulli sub-ode method for the Vakhnenko equation (VE). The results obtained in this work are lump and kink soliton solutions presented in hyperbolic trigonometric and rational functions. This work reveals the effectiveness and future of our method for solving complex solitary wave problems.

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