Lie symmetry analysis and conservation laws for the (2+1)-dimensional Mikhalev equation

Abstract

Lie symmetry analysis is applied to the (2+1)-dimensional Mikhal\"ev equation, which can be reduced to several (1+1)-dimensional partial differential equations with constant coefficients or variable coefficients. Then we construct exact explicit solutions for part of the above (1+1)-dimensional partial differential equations. Finally, the conservation laws for the (2+1)-dimensional Mikhal\"ev equation are constructed by means of Ibragimov's method.