On obtaining analytical soliton solutions of Drinfeld-Sokolov-Satsuma-Hirota equation via two efficient methods

Abstract

Abstract In this work, we use the enhanced modified extended tanh method (eMETEM) and the unified Riccati equation expansion (UREEM) to find analytical solutions to the Drinfeld-Sokolov-Satsuma-Hirota equation (DSSH). The use of coupled nonlinear partial differential equations in the modeling of many physical phenomena, the origin of the Drinfeld-Sokolov-Satsuma-Hirota equation being the formation of the coupled system, and the fact that this model also constitutes a fundamental model in representing numerous physical events, primarily shallow water and coastal regions, have been the driving force behind the study. To visualize the obtained solutions, contour, two and three-dimensional plots are presented. The proposed methods have effectively generated a range of solitons, such as kink, singular, and periodic singular types. The graphic presentations complete the interpretation of the physical significance of the obtained kink and singular soliton types, and the interpretation of the obtained graphs within this framework. In this sense, the findings of the study will help to shape future research in this field.