A super Degasperis–Procesi equation and related integrable systems. (27th January 2021)

• Record Type: Journal Article
• Authors: Gao, Binfang; Tian, Kai; Liu, Qing Ping
• Is Part Of: Proceedings. Volume 477:Number 2245(2021)
• Publication Date: 2021-01-27
• Subjects: reciprocal transformation -- super trace identity -- bi-Hamiltonian structure -- conservation laws; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0780
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : Based on a 4 × 4 matrix spectral problem, a super Degasperis–Procesi (DP) equation is proposed. We show that under a reciprocal transformation, the super DP equation is related to the first negative flow of a super Kaup–Kupershmidt (KK) hierarchy, which turns out to be a particular reduction of a super Boussinesq hierarchy. The bi-Hamiltonian structure of the super Boussinesq hierarchy is established and subsequently produces a Hamiltonian structure, as well as a conjectured symplectic formulation of the super KK hierarchy via suitable reductions. With the help of the reciprocal transformation, the bi-Hamiltonian representation of the super DP equation is constructed from that of the super KK hierarchy. We also calculate a positive flow of the super DP hierarchy and explain its relations with the super KK equation. Infinitely many conservation laws are derived for the super DP equation, as well as its positive flow.