A super Degasperis–Procesi equation and related integrable systems | Zendy

Binfang Gao | Zendy; Kai Tian | Zendy; Qing Ping Liu | Zendy

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A super Degasperis–Procesi equation and related integrable systems

Author(s) -

Binfang Gao,

Kai Tian,

Qing Ping Liu

Publication year - 2021

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2020.0780

Subject(s) - integrable system , hierarchy , mathematics , conservation law , hamiltonian (control theory) , reciprocal , symplectic geometry , mathematical analysis , mathematical physics , pure mathematics , mathematical optimization , linguistics , philosophy , economics , market economy

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.

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