Symmetry and similarity solutions of variable coefficients generalized Zakharov–Kuznetsov equation

摘要

In this paper we propose a compatibility method of finding symmetry and similarity reduction of partial differential equations. Being a simple example, the (2 + 1)-dimensional variable coefficients Zakharov–Kuznetsov equation is considered. As a result, we derive the symmetries and corresponding reductions of the Zakharov–Kuznetsov equation. At the same time some new similarity solutions are obtained. The method can also be applied to other nonlinear evolution equations in mathematical physics.