Lie point symmetries exact solutions and conservation laws of perturbed Zakharov–Kuznetsov equation with higher-order dispersion term

Abstract

In this paper, Zakharov–Kuznetsov equation is investigated for exact solutions and conservation laws. The well-known Zakharov–Kuznetsov equation contains third-order dispersion, so its validity is restricted to the waves of small amplitudes only. When the amplitude of the wave increases, the velocity and the width of the soliton deviate from the prediction of this equation. To overcome this deficiency, higher-order dispersion term is added to the Zakharov–Kuznetsov equation. We obtain Lie point symmetries and conservation laws for this new model. Wave transformation is applied to convert the nonlinear partial differential equation into another nonlinear ordinary differential equation. Then exact solutions are computed for this with sine–cosine method and modified Kudryashov methods. Obtained solutions are new and are of significant importance in the field of plasma physics.