Exact periodic solitary wave solutions for the (2+1)-dimensional Boussinesq equation

Exact periodic solitary wave solutions for the (2+1)-dimensional Boussinesq equation are obtained by using the extended ansätz function method. Detailed behavior of the propagation of the periodic solitary wave solutions for the (2+1)-dimensional Boussinesq equation is illustrated by using the method of figure analysis. The result shows that it is entirely possible for the (2+1)-dimensional integrable equations or non-integrable equations that there exist periodic solitary waves in the different direction. The propagation of the periodic solitary waves is actually phase shifts of solitons, and the amplitudes of non-singular periodic solitary waves depend on frequency and wave number of periodic wave.