Symmetry reductions and exact solutions of a variable coefficient (2+1)-Zakharov-Kuznetsov equation

Abstract

We study the generalized (2+1)-Zakharov-Kuznetsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. The Lie point symmetry generators of a special form of the class of equations are derived. We classify the Lie point symmetry generators to obtain the optimal system of one- dimensional subalgebras of the Lie symmetry algebras. These subalgebras are then used to construct a number of symmetry reductions and exact group-invariant solutions to the underlying equation.