Exact traveling wave solutions and dynamical behavior for the (n + 1)-dimensional multiple sine-Gordon equation

摘要

Using the methods of dynamical systems for the (n+1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.