Exact Solitary Wave Solution of Benjamin-Bona-Mahony and Modified Regularized Long Wave Equations Using Sardar Subequation Method

Lawwal Muduru Sada¹ , Umar Ali Muhammad² , Musa Idris³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.43-49, Jun-2024

Online published on Jun 30, 2024

Copyright © Lawwal Muduru Sada, Umar Ali Muhammad, Musa Idris . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This article explores solutions for the Benjamin-Bona-Mahony (BBM) equation and the Modified Regularized Long Wave (MRLW) equation. The BBM equation serves as a model for the propagation of small-amplitude long waves in one-dimensional space, addressing limitations of the classic Korteweg-de-Vries (KdV) equation, particularly in high wavenumber scenarios. On the other hand, the MRLW equation describes dispersed wave phenomena, such as those observed in shallow water and phonon packets within nonlinear crystals. The solutions to these equations manifest as solitary waves, commonly known as solitons. In this study, we employ the improved Sardar subequation method to comprehensively analyze the resulting solitary waves. We also provided the visual representations for obtained solutions in the forms of absolute value 3D, 2D, and contour plots.

Key-Words / Index Term :
BBM equation, MRLW equation, improved Sardar subequation method, solitary wave, KdV, Shallow water wave

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