A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

Abstract

In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and traveling wave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived.