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.
