Exploration of soliton solution of coupled Drinfel’d–Sokolov–Wilson equation under conformable differential operator

The aim of this paper is to study the nonlinear couple Drinfel’d–Sokolov–Wilson (DSW) equation under conformable differential operator (CDO) that plays an important role in describing the shallow water in fluid mechanics, plasma physics, nonlinear optics and Bose–Einstein condensate (soliton formation). The Tanh-Coth and energy balance techniques are implemented in this work to explore some travelling wave solutions. These analytical methods yield various solutions for the considered DSW equation. The solutions obtained from both method are expressed in the form of hyperbolic and trigonometric function. Furthermore, the dynamic behaviour of the obtained solutions are illustrated, via 2D and 3D curves. Additionally, the effect of the conformable differential operator on dynamics of wave solutions is studied via 2D graphs.