On the Existence of Solitary Wave Solutions for Perturbed Degasperis-Procesi Equation

• Xu, Guoan ^[1] ; Zhang, Yi ^[2]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

     
  2. [2] Huaqiao University

     Huaqiao University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
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• Resumen

  • The Degasperis–Procesi (DP) equation is a significant model of shallow-water waves, which has been well investigated in the current study. Notably, the existence of solitary wave solutions without perturbation has been first proved. However, the persistence of solitary wave solutions of the perturbed DP equation by employing the geometric singular perturbation theory and the Melnikov method has been analyzed. Therefore, the perturbed DP equation possesses a solitary wave solution from the demonstration of having a homoclinic orbit.