Travelling wave solutions for the generalized Zakharov–Kuznetsov equation with higher-order nonlinear terms

With the aid of symbolic computation and two auxiliary ordinary differential equations, the new generalized algebraic method is extended to the generalized Zakharov–Kuznetsov (GZK) equation with higher-order nonlinear terms for constructing a series of new and more general travelling wave solutions. Because of the higher-order nonlinear terms, the equation can not be directly dealt with by the method and require some kinds of techniques. By means of two proper transformations, we transform the GZK equation to an ordinary differential equation that is easy to solve and find a rich variety of new exact travelling wave solutions for the GZK equation, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, combined Jacobi elliptic function solutions and rational function solutions. The method used here can be also extended to other nonlinear partial differential equations with higher-order nonlinear terms.