Travelling wave solutions for a Zakharov–Kuznetsov modified equal width equations

Abstract

We consider a family of generalized Zakharov–Kuznetsov modified equal width equations in (2＋1)-dimensions which involves an arbitrary function and three parameters. By applying the Lie group theory, we perform a complete classification of the Lie point symmetries of these equations depending on the arbitrary elements involved. We carry out symmetry reductions and obtain exact solutions by using the Lie point symmetries admitted by this family. Moreover, we show that this family of equations admits local low-order multipliers. Finally, we derive all local low-order conservation laws of this family through the multiplier approach.