Bifurcations, Exact Peakon, Periodic Peakons and Solitary Wave Solutions of Generalized Camassa-Holm-Degasperis-Procosi Type Equation

Authors：Sun, Xianbo; Li, Jibin^*; Chen, Guanrong

Source：International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2023, 33(10): 2350124.

DOI：10.1142/S0218127423501249

• Bifurcation
• solitary wave
• periodic wave
• peakon
• periodic peakon
• collage of solutions
• generalized Camassa-Holm-Degasperis-Procosi type equation

For the generalized Camassa-Holm-Degasperis-Procosi (CH-DP) type equation, by using the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to analyze its corresponding traveling wave systems, which depend on four parameters, it is found that under different parameter conditions its bifurcation portraits exhibit all possible exact explicit bounded solutions, such as solitary wave solutions, periodic wave solutions, peakon as well as periodic peakons. A total of 30 explicit exact parametric representations of the traveling wave system of the CH-DP type equation are presented.

• Institution
  浙江师范大学; 杭州师范大学