Analysis of the exact solutions of nonlinear coupled Drinfeld–Sokolov–Wilson equation through ϕ6-model expansion method

The coupled Drinfeld–Sokolov–Wilson (DSW) equation is a system of nonlinear partial differential equations (NLPDEs) in (1+1)-dimensions that play a fundamental role in soliton theory and integrable systems. Due to its ability to accurately describe wave phenomena in dispersive water waves, coupled DSW equation has wide-ranging applications in fluid dynamics, plasma physics, and mathematical physics. This study investigates the solitary wave solution of coupled DSW equation by using ϕ6-model expansion. This technique reveals the diverse types of solutions, including bright, dark, singular, and periodic singular solitons. The 3D, contour, and 2D plots are also illustrated to demonstrate the physical behavior of the obtained solutions. The findings of this study can contribute to the development of new analytical and numerical tools for solving other nonlinear equations in the future. The inclusion of constraint conditions in the ϕ6-model expansion technique enhances its applicability and reliability, rendering it a valuable approach for investigating nonlinear systems in various scientific domains.