A Super Camassa–Holm Equation with N‐Peakon Solutions. Issue 1 (12th July 2012)

• Record Type: Journal Article
• Authors: Geng, Xianguo; Xue, Bo; Wu, Lihua
• Is Part Of: Studies in applied mathematics. Volume 130:Issue 1(2013)
• Page Start: 1
• Page End: 16
• Publication Date: 2012-07-12
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/j.1467-9590.2012.00555.x
• Languages: English
• ISSNs: 0022-2526

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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 <italic>N</italic> 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.</p> </abstract>