Construction of soliton and multiple soliton solutions to the longitudinal wave motion equation in a magneto-electro-elastic circular rod and the Drinfeld-Sokolov-Wilson equation

Abstract

The present paper implements the novel generalized (G'/G)-expansion approach in solving the most popular nonlinear wave equations such as the longitudinal wave motion equation in a magneto-electro-elastic circular rod and the Drinfeld-Sokolov-Wilson equation. In this regard, we investigate the method to obtain new type of wave solutions of the studied models. New exact wave solutions are derived in the structures such as singular bright solition, compaction, singular bright periodic wave solitions, singular dark solition and singular dark periodic wave solition solutions of the studied models by using the novel generalized (G'/G)-expansion scheme. To draw the physical aspect of the got results, the 2D, 3D surfaces as well as the relating the contour plot surfaces of some acquired results are performed. The obtained results can assist to illustrate the physical application of the examined models and other nonlinear physical models appearing in mathematical physics.