Abstract
The dynamics of solitary waves in the presence of perturbation terms is studied in this paper with the aid of the semi-inverse variational principle. In this paper, shallow water waves as well as internal gravity waves in a density-stratified ocean are considered. These are respectively modeled by the Korteweg-de Vries equation as well as the compound Korteweg-de Vries equation. An analytical solution of the solitary wave is found in each case.