An approximate sine-Gordon equation and its traveling wave solution in (n+1)-dimensional space

摘要

In this paper, we apply the Painlevé analysis to the study of an approximate sine-Gordon equation and obtain the traveling solitary wave solution in (n+1)-dimensional space explicitly, which is significantly different from one which is found in our last work. The technique described herein can also be applied to other nonlinear evolution equations such as the KdV-type equation and the nonlinear Schrödinger equation in higher-dimensional space.