Exploration of nonlinear traveling wave phenomena in quintic conformable Benney-Lin equation within a liquid film

Noorah Mshary; Noorah Mshary

doi:10.3934/math.2024542

AIMS Mathematics

2024, Volume 9, Issue 5: 11051-11075. doi: 10.3934/math.2024542

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Exploration of nonlinear traveling wave phenomena in quintic conformable Benney-Lin equation within a liquid film

Noorah Mshary ^,

Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia

Received: 20 January 2024 Revised: 29 February 2024 Accepted: 04 March 2024 Published: 20 March 2024
MSC : 33B15, 34A34, 35A20, 35A22, 44A10

In this article, we use the modified extended direct algebraic method (mEDAM) to explore and analyze the traveling wave phenomena embedded in the quintic conformable Benney-Lin equation (CBLE) that regulates liquid film dynamics. The proposed transformation-based approach developed for nonlinear partial differential equations (PDEs) and fractional PDEs (FPDEs), efficiently produces a plethora of traveling wave solutions for the targeted CBLE, capturing the system's nuanced dynamics. The methodically determined traveling wave solutions are in the form of rational, exponential, hyperbolic and trigonometric functions which include periodic waves, bell-shaped kink waves and signal and double shock waves. To accurately depict the wave phenomena linked to these solutions, we generate 2D, 3D, and contour graphs. These visualizations not only improve understanding of the CBLE model's dynamics, but also provide a detailed way to examine its behavior. Moreover, the use of the proposed techniques contributes to a better understanding of the other FPDEs' distinct characteristics, enhancing our comprehension of their underpinning dynamics.
Citation: Noorah Mshary. Exploration of nonlinear traveling wave phenomena in quintic conformable Benney-Lin equation within a liquid film[J]. AIMS Mathematics, 2024, 9(5): 11051-11075. doi: 10.3934/math.2024542

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Abstract

In this article, we use the modified extended direct algebraic method (mEDAM) to explore and analyze the traveling wave phenomena embedded in the quintic conformable Benney-Lin equation (CBLE) that regulates liquid film dynamics. The proposed transformation-based approach developed for nonlinear partial differential equations (PDEs) and fractional PDEs (FPDEs), efficiently produces a plethora of traveling wave solutions for the targeted CBLE, capturing the system's nuanced dynamics. The methodically determined traveling wave solutions are in the form of rational, exponential, hyperbolic and trigonometric functions which include periodic waves, bell-shaped kink waves and signal and double shock waves. To accurately depict the wave phenomena linked to these solutions, we generate 2D, 3D, and contour graphs. These visualizations not only improve understanding of the CBLE model's dynamics, but also provide a detailed way to examine its behavior. Moreover, the use of the proposed techniques contributes to a better understanding of the other FPDEs' distinct characteristics, enhancing our comprehension of their underpinning dynamics.

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