Multi-wave, breather and interaction solutions to (3+1) dimensional Vakhnenko–Parkes equation arising at propagation of high-frequency waves in a relaxing medium

Abstract

In this study, based on the Hirota bilinear form, the exact analytic solutions of the (3 + 1) dimensional Vakhnenko-Parkes equation with various physical properties were constructed with the help of the Maple package program and symbolic computation. These solutions are the type of multi-waves, breather wave, lump-kink, lump-periodic solutions and interaction solutions (between lump and hyperbolic wave solutions). The constructed solutions have expanded and enriched the solution forms of this new model existing in the literature. By means of Maple package program, 3D and 2D graphs were drawn for the special choices of the parameters in the solutions, and the physical structures of the solutions obtained in this way were also observed. The solutions obtained can be used in the explanation of physical phenomena occurring in the propagation of high-frequency waves in a relaxing medium.