Travelling waves solutions of the KP equation in weakly dispersive media

Abstract

The current work focuses on the solutions of the Kadomtsev and Petviashvili (KP) equation, which models nonlinear waves in a dispersive medium. The modified auxiliary equation approach is utilized to find analytical solutions of the KP equation. Consequently, a set of solutions including Jacobi elliptic solutions and solitary and periodic waves solutions is obtained. The geometry of the derived solutions is plotted with an appropriate choice of the parameters. It can be seen that the proposed method is powerful and can be used to solve nonlinear partial differential equations due to its simplicity.

Keywords

• the kp equation
• exact solution
• the modified auxiliary equation method