Copyright © 2011 Shengqiang Tang and Shu Xia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using the bifurcation theory of dynamical systems, we study the coupled Higgs field equation and the existence of new solitary wave solutions, and uncountably infinite many periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the above waves are determined.