Dynamical Behavior and Exact Explicit Traveling Wave Solutions of a Generalized Vakhnenko-Parkes Equation

Jibin Li; Ai Ke

Ayuda

Dynamical Behavior and Exact Explicit Traveling Wave Solutions of a Generalized Vakhnenko-Parkes Equation

Jibin Li ^[1] ; Ai Ke ^[2]
1. [1] Zhejiang Normal University
  
  Zhejiang Normal University
  
  China
2. [2] Donghua University
  
  Donghua University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
Idioma: inglés
Enlaces
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Resumen
- This paper aims to find exact explicit traveling wave solutions of the generalized Vakhnenko-Parkes (VP) equation. Using the singular traveling wave equation theory and dynamical system method, we find the bifurcations of phase portraits and derive the dynamical behavior of the corresponding traveling wave system. Under different parameter conditions, exact explicit solitary wave solution, periodic wave solution, periodic peakons as well as kink and anti-kink wave solutions can be found. By comparing with the previous studies of the generalized VP equation, it can be found that the kink and anti-kink wave solutions are the new solutions of the generalized VP equation studied in this paper.
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