Bidirectional solitary wave solutions and soliton solutions for two nonlinear evolution equations

The homogeneous balance method for constructing solitary wave solutions and soliton solutions is further developed on obtaining quasi-solution by using step-by-step principle. The main advantage of the extended approach is to avoid the problem of "intermediate expression swell". The effectiveness of the method is demonstrated by application to the generalized Boussinesq equation and the bidirectional Kaup-Kupershmidt equation. The one-soliton, two-soliton and three-soliton solutions with multipe collisions are derived for these two equations with the assistance of Maple.