Bifurcations and Exact Peakons, Periodic Peakons, Solitary Wave, Kink Wave Solutions for the Quartic CH-Type Equation

• Xueqiong Yi ^[1] ; Yuqian Zhou ^[1] ; Qian Liu ^[1] ; Kebing Li ^[1] ; Shengning Zhang ^[1]
  1. [1] Chengdu University of Information Technology

     Chengdu University of Information Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
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• Resumen

  • We introduce a novel quartic Camassa-Holm type equation and address their traveling wave solutions. The difficulties related to the non-analytical vector fields and complex elliptic integrals are overcome by using the theory of singular traveling wave systems. Upon analyzing the bifurcations of the traveling wave solutions, we study the phase portraits of different topologies, and obtain some exact traveling wave solutions including peakons, periodic peakons, solitary waves, and kink wave solutions. Our results are useful to better understand wave phenomena described by partial differential equations with higher-order nonlinear terms, and pave the way to obtain the traveling wave solutions of other equations with similar nonlinear terms.