Analytical wave solutions for the nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and two-dimensional Kadomtsev-Petviashvili-Burgers equations

Abstract

In this work, we study the procedure involved in applying the extended (G′(ϕ)G(ϕ))-expansion method in solving nonlinear partial differential equations. The method depends on the auxiliary equation (G″(ϕ)=-(αG′(ϕ)+βG(ϕ))) which the general solution is liable on three conditions (α2-4β>0,α2-4β<0,α2-4β=0). We implement this method to construct the wave solutions of the nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and the two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equations. We obtain wave solutions in the form of hyperbolic and trigonometric functions of the two equations. The calculations carried out in this work have been proven and confirmed with the aid of Mathematica software. Also, the study reviewed the superiority of the method compared to extended direct algebraic method, extended direct algebraic mapping and extended Sech-tanh methods. Keywords: The three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation, The two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equation, Wave solutions