Soliton solutions for Boussinesq-like equations with spatio-temporal dispersion

This paper addresses the soliton solutions for a variety of Boussinesq-like equations with spatio-temporal dispersion. The semi-inverse variational principle (SVP) is applied to obtain these solutions. The derived solutions address the dynamics of thin inviscid layers with free surface, solitons solutions, and other nonlinear phenomena. The structures of the obtained solutions were carried out and illustrated, and can provide feasible basis for studying surface water models.