Travelling Wave Solutions to the Space-Time Fractional ZKBBM Equation in Mathematical Physics

Md. Munnu Miah., Md Al Amin Meia., Pranab Majumder., Tajbeha Fatema., Md Mahmudul Hasan Pranto. and Ahammodullah Hasan
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Md. Munnu Miah.: Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh.
Md Al Amin Meia.: Department of Mathematics, Government Titumir College, Dhaka-1213, Bangladesh.
Pranab Majumder.: Department of Mathematics, Lamar University, Beaumont, Texas, USA.
Tajbeha Fatema.: Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh.
Md Mahmudul Hasan Pranto.: Institute of Statistical Research and Training (ISRT), University of Dhaka, Dhaka, Bangladesh.
Ahammodullah Hasan: Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh.

International Journal of Research and Innovation in Applied Science, 2024, vol. 9, issue 7, 164-174

Abstract: This paper focuses on the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation, which serves as a notable model for various phenomena such as water wave mechanics, shallow water waves, quantum mechanics, ion-acoustic waves in plasma, electro-hydro-dynamical models for local electric fields, and signal processing waves through optical fibers. We employ the exp(-τ(ξ)) -expansion approach, aided by travelling wave transformations, to ascertain the helpful and more comprehensive accurate travelling wave solutions to those above nonlinear differential equations (NLDEs). Additionally, we elucidate the physical relevance of the acquired solutions by determining the precise values of the relevant parameters and representing them graphically to gain insight into the underlying physical processes. Finally, we demonstrate that the exp(-τ(ξ)) -expansion approach is advantageous, potent, uncomplicated, and yields more comprehensive answers. It can also assist in analyzing a wide range of travelling wave solutions for various types of nonlinear differential equations.

Date: 2024
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