Dark and bright hump solitons in the realm of the quintic Benney-Lin equation governing a liquid film

Waleed Hamali; Hamad Zogan; Abdulhadi A. Altherwi; Waleed Hamali; Hamad Zogan; Abdulhadi A. Altherwi

doi:10.3934/math.20241414

AIMS Mathematics

2024, Volume 9, Issue 10: 29167-29196. doi: 10.3934/math.20241414

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Dark and bright hump solitons in the realm of the quintic Benney-Lin equation governing a liquid film

1.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi Arabia
2.
Department of Computer Science, College of Computer Science and Information Technology, Jazan University, Jazan, Kingdom of Saudi Arabia
3.
Department of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan, Kingdom of Saudi Arabia

Received: 23 August 2024 Revised: 24 September 2024 Accepted: 27 September 2024 Published: 15 October 2024
MSC : 34G20, 35A20, 35A22, 35R11

This study explored and examined soliton solutions for the Quintic Benney-Lin equation (QBLE), which describes the dynamic of liquid films, using the Riccati modified extended simple equation method (RMESEM). The proposed approach, which is designed for nonlinear partial differential equations (NPDEs), effectively generates a large number of soliton solutions for the given QBLE, which basically captures the fundamental dynamics of the system. The rational, hyperbolic, rational-hyperbolic, trigonometric, and exponential forms of the scientifically specified soliton solutions are the main determinants of the hump solitons. We used 2D, 3D, and contour visualizations to offer accurate representations of the researched soliton phenomena associated with these solutions. These representations revealed the existence of dark and bright hump solitons in the framework of the QBLE and offer a thorough way to examine the model's behavioral characteristics in the liquid film by analyzing the QBLE model's soliton dynamics. Moreover, applying the suggested approach advances our knowledge of the unique features of the other similar NPDEs and the underlying dynamics.
Citation: Waleed Hamali, Hamad Zogan, Abdulhadi A. Altherwi. Dark and bright hump solitons in the realm of the quintic Benney-Lin equation governing a liquid film[J]. AIMS Mathematics, 2024, 9(10): 29167-29196. doi: 10.3934/math.20241414

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Abstract

This study explored and examined soliton solutions for the Quintic Benney-Lin equation (QBLE), which describes the dynamic of liquid films, using the Riccati modified extended simple equation method (RMESEM). The proposed approach, which is designed for nonlinear partial differential equations (NPDEs), effectively generates a large number of soliton solutions for the given QBLE, which basically captures the fundamental dynamics of the system. The rational, hyperbolic, rational-hyperbolic, trigonometric, and exponential forms of the scientifically specified soliton solutions are the main determinants of the hump solitons. We used 2D, 3D, and contour visualizations to offer accurate representations of the researched soliton phenomena associated with these solutions. These representations revealed the existence of dark and bright hump solitons in the framework of the QBLE and offer a thorough way to examine the model's behavioral characteristics in the liquid film by analyzing the QBLE model's soliton dynamics. Moreover, applying the suggested approach advances our knowledge of the unique features of the other similar NPDEs and the underlying dynamics.

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