Travelling wave solutions of Drinfel’d–Sokolov–Wilson, Whitham–Broer–Kaup and (2+1)-dimensional Broer–Kaup–Kupershmit equations and their applications

Abstract In this paper, some new exact travelling wave solutions are constructed in different form of coupled partial differential equations having terms of odd and even order partial derivative, by applying modified extended direct algebraic method. Traveling wave solutions are found in the form of solitons, bell and anti-bell periodic, bright and dark solitary wave etc, which have many applications in physics and other areas of applied sciences. Furthermore, more coupled nonlinear PDEs can also be solved by this method. The coupled nonlinear Drinfel’d–Sokolov–Wilson, Whitham–Broer–Kaup and (2+1)-dimensional Broer–Kaup–Kupershmit equations are selected to show the effectiveness of this method.

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