On lump and solitonic wave structures for the (3+1)-dimensional nonlinear evolution model

Abstract

In order to understand many complex situations in wave propagation, such as heat transfer, fluid dynamics, optical fibers, electrodynamics, physics, chemistry, biology, condensed matter physics, ocean engineering, and many other branches of nonlinear science, the majority of natural processes are routinely modelled and analysed using nonlinear evolution equations. In this study, the (3+1)-dimensional nonlinear evolution equation is investigated analytically. Initially, the Hirota bilinear approach is used to develop the bilinear version of the higher dimensional nonlinear model. Consequently, we are able to design periodic wave soliton solutions, lump wave and single-kink soliton solutions, and collisions between lumps and periodic waves. Later on, the unified method is applied to develop several new travelling wave solutions for the governing model substantially. Furthermore, numerous exact solutions are analyzed graphically to explore many fascinating nonlinear dynamical structures with the aid of 3D, contour, and 2D visualizations. A variety of higher dimensional nonlinear evolution models can also be investigated by employing present approaches arising in many fields of contemporary science and technology.