Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law

Mengke Yu, Cailiang Chen and Qiuyan Zhang ()
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Mengke Yu: College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China
Cailiang Chen: College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China
Qiuyan Zhang: College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China

Mathematics, 2023, vol. 11, issue 20, 1-28

Abstract: In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavior of the associated regular system and we obtain bifurcations of the phase portraits of the traveling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, and the peakon, homoclinic and heteroclinic solutions.

Keywords: periodic solutions; peakon; homoclinic orbit; heteroclinic orbit; the generalized Radhakrishnan–Kundu–Lakshmanan equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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