Traveling wave solutions for the $$(2+1)$$-dimensional generalized Zakharov–Kuznetsov equation with variable coefficients

Abstract

In this article, the unified method, the improved F-expansion method and the modified Kudryashov method are used to obtain the traveling wave solutions of the generalized Zakharov–Kuznetsov equation with variable coefficients. Different types of traveling wave solutions are derived including polynomial solutions and rational solutions by applying the unified method. The polynomial solutions include solitary wave solutions, soliton wave solutions and elliptic wave solutions, and the rational solutions contain periodic type rational solutions and soliton type rational solutions. By means of the improved F-expansion method with Riccati equation, the hyperbolic trigonometric solutions, trigonometric solutions and rational solutions are obtained containing several free parameters. The modified Kudryashov method is also applied to obtain new traveling wave solutions. In addition, the properties of several solutions are represented graphically with the appropriate parameters.