On the breather waves, lump solutions, two-wave solutions of ([formula omitted]) dimensional Martínez Alonso–Shabat equation

Abstract

We effectively utilize Hirota’s bilinear method (HBM) in this article to scrutinize the diverse wave profiles to the (3+1) dimensional Martínez Alonso–Shabat equation when the test function approaches are taken into consideration. Several novel breather waves, lump solutions, and two-wave solutions are obtained. Furthermore, with the assistance of appropriate parameters, the reported results’ physical behavior is sketched out in several 3 dimensional, 2 dimensional, and contour profiles. The obtained results are useful in grasping the fundamental scenarios of nonlinear sciences as well as the related nonlinear higher dimensional wave fields, both of which are important. With the help of Mathematica, the obtained results are verified by inserting them into the governing equation. Thus, our programmes, which are based on the fortress of representative calculations, provide a robust mathematical framework for resolving difficult nonlinear wave problems.