A Degasperis-Procesi equation II with multi-peakon solutions

被引：0
|
作者：
Xue, Bo [1 ]
Du, Huiling [1 ]
Geng, Xianguo [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, 100 Kexue Rd, Zhengzhou 450001, Henan, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2021年 / 121卷
基金：
中国国家自然科学基金;
关键词：
Degasperis-Procesi equation II; Multi-peakon; Dynamical system; Hamiltonian structures; Conservation laws;
D O I：
10.1016/j.aml.2021.107463
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Based on a 3 x 3 matrix spectral problem, a new hierarchy of nonlinear evolution equations is obtained by means of the zero-curvature equation and the Lenard recursion equation. With the help of the trace identity, the Hamiltonian structures of this hierarchy are established. Then a new nonlinear wave equation, called the Degasperis-Procesi equation II, is derived from a negative flow, which admits exact solutions with N-peakons. Finite-dimensional dynamical systems related to N-peakon solutions and an infinite sequence of conserved quantities of the Degasperis-Procesi equation II are obtained. (C) 2021 Elsevier Ltd. All rights reserved.
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