Multiplicity of kink and hump structures in Van der Waals gas system

Rashid Ali; Rabia Imtiaz; Moin-ud-Din Junjua; Fuad A. Awwad; Emad A. A. Ismail; Ahmed S. Hendy; Rashid Ali; Rabia Imtiaz; Moin-ud-Din Junjua; Fuad A. Awwad; Emad A. A. Ismail; Ahmed S. Hendy

doi:10.3934/math.2025564

AIMS Mathematics

2025, Volume 10, Issue 5: 12493-12518. doi: 10.3934/math.2025564

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Multiplicity of kink and hump structures in Van der Waals gas system

1.
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
2.
Department of Mathematics, University of Engineering and Technology, Lahore 39161, Pakistan
3.
Department of Mathematics, Ghazi University, Dera Ghazi Khan 32200, Pakistan
4.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
5.
Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia
6.
Department of Mechanics and Mathematics, Western Caspian University, Baku 1001, Azerbaijan

Received: 21 March 2025 Revised: 03 May 2025 Accepted: 09 May 2025 Published: 28 May 2025
MSC : 34G20, 35A20, 35A22, 35R11

In this work, numerous features of the nonlinear Van der Waals gas system in the sense of viscosity capillarity are analytically and theoretically investigated. A novel trustworthy integrating approach, namely the Riccati modified extended simple equation method (RMESEM), is utilized to determine the physical nature of the system. This technique successfully generates a novel range of kink, anti-kink, cuspon kink, and bell-shaped bright and dark hump solitary wave solutions in the form of exponential, periodic, hyperbolic, rational, and rational-hyperbolic functions. Using suitable parameter values that satisfy constraint criteria, we generate a set of 2D graphs to improve comprehension and graphically depict these solitary wave solutions. The efficiency and adaptability of our method in solving a range of nonlinear problems in mathematical science and engineering are validated by our computational research.
Citation: Rashid Ali, Rabia Imtiaz, Moin-ud-Din Junjua, Fuad A. Awwad, Emad A. A. Ismail, Ahmed S. Hendy. Multiplicity of kink and hump structures in Van der Waals gas system[J]. AIMS Mathematics, 2025, 10(5): 12493-12518. doi: 10.3934/math.2025564

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Abstract

In this work, numerous features of the nonlinear Van der Waals gas system in the sense of viscosity capillarity are analytically and theoretically investigated. A novel trustworthy integrating approach, namely the Riccati modified extended simple equation method (RMESEM), is utilized to determine the physical nature of the system. This technique successfully generates a novel range of kink, anti-kink, cuspon kink, and bell-shaped bright and dark hump solitary wave solutions in the form of exponential, periodic, hyperbolic, rational, and rational-hyperbolic functions. Using suitable parameter values that satisfy constraint criteria, we generate a set of 2D graphs to improve comprehension and graphically depict these solitary wave solutions. The efficiency and adaptability of our method in solving a range of nonlinear problems in mathematical science and engineering are validated by our computational research.

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