Generalized double sinh-Gordon equation: Symmetry reductions, exact solutions and conservation laws

Document Type : Regular Paper


1 School of Computer, Statistical and Mathematical Sciences, North-West University, Potchefstroom Campus, Private Bag X 2520, Republic of South Africa

2 International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa


This paper aims to study a generalized double sinh-Gordon equation, which appears in several physical phenomena such as integrable quantum field theory, kink dynamics and fluid dynamics. Lie symmetry analysis together with the simplest equation method is used to obtain exact solutions for this equation. Moreover, we derive conservation laws for the equation by using two different approaches, namely, the direct method and the new conservation theorem due to Ibragimov.