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