The solitary wave solutions of the nonlinear perturbed shallow water wave model

Abstract In this paper, we study the nonlinear perturbed shallow water wave model, which satisfies the asymptotic integrability condition with this family: the KdV equation, Camassa–Holm equation and Degasperis-Procesi equation. We establish the existence of solitary wave solutions for the perturbed nonlinear dispersive equations by means of the geometric singular perturbation and invariant manifold theory.