A novel (3+1)-dimensional sine-Gorden and a sinh-Gorden equation: Derivation, symmetries and conservation laws

In this paper, a novel (3+1)-dimensional sine-Gorden and a sinh-Gorden equation are derived. These two equations are derived for the first time from the extended (3+1) dimensional zero curvature equation, using the compatibility condition. Then the infinitesimal transformation of this equation is studied from the symmetry point of view. Meanwhile, it turns out that these two equations can be reduced to the classical sin-Gordon equation and the sinh-Gordon equation. Some analytic solutions are presented by means of traveling wave transformation. Finally, based on the multiplier method, a conservation law is obtained. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

A novel (3+1)-dimensional sine-Gorden and a sinh-Gorden equation are derived for the first time from the extended (3+1) dimensional zero curvature equation, with their symmetry and reduction to classical equations explored. Analytic solutions are presented through traveling wave transformation, and a conservation law is obtained using the multiplier method.