Symmetry analysis and exact Jacobi elliptic solutions for the nonlinear couple Drinfeld Sokolov Wilson dynamical system arising in shallow water waves

Abstract

We adopted the Lie symmetry technique to obtain some new exact waveform solutions for the coupled Drinfeld Sokolov Wilson (DSW) system. This system emerges from phenomena such as water waves, theoretical physics, fluid dynamics, biology, and chemical sciences. We use the Jacobi elliptic function (JEF) method to deal with some of the reduced systems during the symmetry reductions, which reveals rational, exponential, and hyperbolic functions based waveform solutions. The properties of these solutions indicate that these are periodic waves, solitary waves, double periodic waves, and shock wave solutions. Several of the answers that have been found are entirely new and might be important for researchers to recognize. By assigning specific values to parameters, some chosen solutions are graphically validated. This method can be applied more broadly to handle several different types of nonlinear evolution systems.

Keywords

• Lie symmetry technique
• Drinfeld Sokolov Wilson system
• Jacobi elliptic function method
• Nonlinear evolution systems
• Shock waves