A super Degasperis-Procesi equation and related integrable systems

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 su...

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Published inProceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 477; no. 2245; p. 20200780
Main Authors Gao, Binfang, Tian, Kai, Liu, Qing Ping
Format Journal Article
LanguageEnglish
Published England The Royal Society Publishing 01.01.2021
Subjects
super trace identity
conservation laws
bi-Hamiltonian structure
reciprocal transformation
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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.
AbstractList 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.
Author Tian, Kai
Gao, Binfang
Liu, Qing Ping
AuthorAffiliation 1 Faculty of Applied Mathematics, Shanxi University of Finance and Economics , Taiyuan 030006, People’s Republic of China
2 Department of Mathematics, China University of Mining and Technology , Beijing 100083, People’s Republic of China
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Keywords super trace identity
conservation laws
bi-Hamiltonian structure
reciprocal transformation
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One contribution to the special feature ‘Hamiltonian and algebraic structures of finite and infinite dimensional Integrable Systems’ edited by Andrew Hone, Yuji Kodama, Qing Ping Liu, Sara Lombardo and Vladimir Novikov.
Dedicated to Professor Allan P. Fordy on the occasion of his 70th birthday.
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Snippet 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...
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...
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...
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Title A super Degasperis-Procesi equation and related integrable systems
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