Investigation of the analytical and numerical solutions with bifurcation analysis for the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili equation

Abstract

In this work, we investigate the solutions of the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation by three powerful analytical methods: the $$\exp _{a}$$ exp a function method, the $$(\frac{G'}{G})$$ ( G ′ G ) -expansion method, and the Sine-Gordon expansion method. This equation describes the nonlinear wave propagation in many applications like waves of evolutionary shallow water, electrical networks, and engineering devices. Moreover, we study the solutions numerically via the finite difference method. We analyze the bifurcation of dynamical system resulting from the BKP equation. Finally, the majority of our solutions are displayed graphically to present the strength of imposed methods.