Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel–Korteweg–de Vries equation*

Abstract

The Schamel-KdV equation is investigated by the approach of dynamical system. By investigating the dynamical behaviors with phase space analyses, the existences of solitary wave including ω-shape solitary wave and periodic wave are proved. The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given. All possible exact explicit parametric representations of the waves also are presented. Along with the details of the analyses, the analytical results are numerical simulated lastly.