Traveling Wave Solutions of Generalized Dullin–Gottwald–Holm Equation with Parabolic Law Nonlinearity

• Zhang, Yijian ^[1] ; Xia, Yonghui ^[1]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

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

  • With bifurcation method of dynamical system, we investigate the travelling wave solutions of the generalized Dullin–Gottwald–Holm equation (G-DGH) with parabolic law nonlinearity. Based on phase portraits, all possible exact expressions of traveling wave solutions are obtained including compactons, peakons, periodic peakons, periodic wave solutions, solitary wave solutions and kink (or anti-kink) wave solutions.

    The core of bifurcation analysis is the changes of parameters cause the change of topology of the traveling wave system, and so give different exact solutions. Finally, we summarize our results into a theorem.