Modified homogeneous balance method: Applications and new solutions

This work is devoted to application of the modified homogeneous balance method to obtain generalized bilinear forms of some well-known soliton equations: the Korteweg de Vries equation, the scalar Boussinesq equation and the Kaup–Boussinesq equations. These bilinear forms are solved for new solutions using the perturbation method and the principle of superposition.