Exact solutions with solitary patterns for the Zakharov–Kuznetsov equations with fully nonlinear dispersion

In this paper, the nonlinear dispersive Zakharov–Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established.