A Degasperis–Procesi equation II with multi-peakon solutions. (November 2021)

• Record Type: Journal Article
• Authors: Xue, Bo; Du, Huiling; Geng, Xianguo
• Is Part Of: Applied mathematics letters. Volume 121(2021)
• Publication Date: 2021-11
• Subjects: Degasperis–Procesi equation II -- Multi-peakon -- Dynamical system -- Hamiltonian structures -- Conservation laws; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107463
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Based on a 3 × 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.