Solitary wave solution and conservation laws of higher dimensional Zakharov‐Kuznetsov equation with nonlinear self‐adjointness

Abstract

In this paper, we consider (1 + n)‐dimensional Zakharov‐Kuznetsov (ZK) equation for nonlinear self‐adjointness and symmetries. It is proved that the equation is nonlinearly self‐adjoint and its symmetries are computed. The conservation laws are obtained by using new general conservation theorem of Ibragimov for (1 + n)‐dimension and particularly for (1 + 3)‐dimensional ZK equation. Multiplier method is also used to find more conservation laws for (1 + 3)‐dimensional ZK equation and symmetry reduction technique is used to calculate the solitary wave solution.