A Degasperis–Procesi equation II with multi-peakon solutions. (November 2021) - Xue, Bo; Du, Huiling; Geng, Xianguo
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.