Exact Solutions and Conservation Laws for a Generalized Double Combined sinh-cosh-Gordon Equation

Abstract

In this paper we study a generalized double combined sinh-cosh-Gordon equation, which appears in a wide range of physical applications. It admits geometric interpretation as the differential equation which determines time-like surfaces of constant positive curvature in the same spaces. We first compute the optimal system of one-dimensional subalgebras and then use it to obtain the optimal system of group-invariant solutions for the equation. We employ Lie group method along with the simplest equation method to investigate travelling wave solutions for this equation. In addition conservation laws are constructed using two different techniques, namely, the new conservation theorem and the multiplier method.