A study of solitary waves by He's semi-inverse variational principle

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.