The powerful closed form technique for the modified equal width equation with numerical simulation

Abdulhamed Alsisi; Abdulhamed Alsisi

doi:10.3934/math.2025502

AIMS Mathematics

2025, Volume 10, Issue 5: 11071-11085. doi: 10.3934/math.2025502

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The powerful closed form technique for the modified equal width equation with numerical simulation

Abdulhamed Alsisi ^,

Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

Received: 21 March 2025 Revised: 27 April 2025 Accepted: 08 May 2025 Published: 15 May 2025
MSC : 76B25, 35C05, 35C07, 35Q35, 35Q53, 65M20

This work introduces the closed form approach to generate solitary wave solutions to the modified equal width (MEW) model. This model generalizes the equal width (EW) equation, which characterizes wave propagation in shallow water. It aims to better represent nonlinear and dispersive effects by altering the original model's terms. Because of its simplicity, reliability, and efficiency, the proposed technique has the potential to be applied to a range of nonlinear partial differential equations (NPDEs) in practical research. We also employ the finite difference method to provide the numerical solution for the MEW model. A comparison with the analytical solution we arrived at demonstrates the method's accuracy. This work shows that the numerical method stays stable and accurate despite alterations in time stepping, wave speed, and spatial discretization. This also allows further exploration of nonlinear models that accurately depict significant physical processes in our everyday existence.
- closed form approach,
- soliton solutions,
- MEW model,
- extended tanh method,
- numerical methods,
- fluid dynamics
Citation: Abdulhamed Alsisi. The powerful closed form technique for the modified equal width equation with numerical simulation[J]. AIMS Mathematics, 2025, 10(5): 11071-11085. doi: 10.3934/math.2025502

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Abstract

This work introduces the closed form approach to generate solitary wave solutions to the modified equal width (MEW) model. This model generalizes the equal width (EW) equation, which characterizes wave propagation in shallow water. It aims to better represent nonlinear and dispersive effects by altering the original model's terms. Because of its simplicity, reliability, and efficiency, the proposed technique has the potential to be applied to a range of nonlinear partial differential equations (NPDEs) in practical research. We also employ the finite difference method to provide the numerical solution for the MEW model. A comparison with the analytical solution we arrived at demonstrates the method's accuracy. This work shows that the numerical method stays stable and accurate despite alterations in time stepping, wave speed, and spatial discretization. This also allows further exploration of nonlinear models that accurately depict significant physical processes in our everyday existence.

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