Solitary Wave Solutions for the Higher Dimensional Jimo-Miwa Dynamical Equation via New Mathematical Techniques

Abstract

In this study, under the considerations of symbolic computation with the help of Mathematica software, various types of solitary wave solutions for the (3 + 1)-dimensional Jimo–Miwa (JM) equation are successfully constructed based on the extended modified rational expansion method. The constructed solutions are novel and more general for the JM equation named kink wave solutions, anti-kink wave solutions, bright and dark solutions, mixed solutions in the shape of bright-dark solutions, and periodic waves, which do not exist in the existing literature. The physical phenomena of the demonstrated results is represented graphically by two-dimensional, three-dimensional, and contour images with the help of Mathematica. The obtained results will be widely used to explain the various interesting physical structures in the areas of optics, plasma, gas, acoustics, classical mechanics, fluid dynamics, heat transfer, and many others.

Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation

“…In this research, we explored the multiple solitary wave solutions named anti-kink soliton, travelling wave solutions, bright soliton, kink soliton, dark soliton, kink bright and dark solitons, anti-kink bright and dark solitons for nonlinear ZK-MEW equation under the consideration of extended modified rational expansion technique [52][53][54], these type of solutions are novel and does not match with existing literatures.…”