By using the theory of planar dynamical systems to a coupled nonlinear wave equation, the existence of bell-shaped solitary wave solutions, kink-shaped solitary wave solutions, and periodic wave solutions is obtained. Under the different parametric values, various sufficient conditions to guarantee the existence of the above solutions are given. With the help of three different undetermined coefficient methods, we investigated the new exact explicit expression of all three bell-shaped solitary wave solutions and one kink solitary wave solutions with nonzero asymptotic value for a coupled nonlinear wave equation. The solutions cannot be deduced from the former references.
"New Exact Solitary Wave Solutions of a Coupled Nonlinear Wave Equation." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/301645