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A Super Camassa–Holm Equation with N ‐Peakon Solutions
Author(s) -
Geng Xianguo,
Xue Bo,
Wu Lihua
Publication year - 2013
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2012.00555.x
Subject(s) - peakon , camassa–holm equation , mathematics , hierarchy , curvature , matrix (chemical analysis) , lax pair , mathematical physics , mathematical analysis , integrable system , chemistry , geometry , chromatography , economics , market economy
A super Camassa–Holm equation with peakon solutions is proposed, which is associated with a 3 × 3 matrix spectral problem with two potentials. With the aid of the zero‐curvature equation, we derive a hierarchy of super Harry Dym type equations and establish their Hamiltonian structures. It is shown that the super Camassa–Holm equation is exactly a negative flow in the hierarchy and admits exact solutions with N peakons. As an example, exact 1‐peakon solutions of the super Camassa–Holm equation are given. Infinitely many conserved quantities of the super Camassa–Holm equation and the super Harry Dym type equation are, respectively, obtained.