A new 3-component Degasperis–Procesi hierarchy

We propose a new 3-component Degasperis–Procesi (3-DP) system. By investigating the bi-Hamiltonian structure of the corresponding hierarchy, we find that the Hamiltonian functionals of the 3-DP hierarchy are local in the negative direction and homogeneous in both directions. We show that the 3-DP sy...

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Bibliographic Details
Published inPhysica. D Vol. 449; p. 133763
Main Author Li, Nianhua
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2023
Subjects
bi-Hamiltonian structure
Bäcklund transformation
Camassa–Holm equation
Darboux transformation
Reciprocal transformation
Reciprocal transformation
Camassa–Holm equation
bi-Hamiltonian structure
Bäcklund transformation
Darboux transformation
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Summary:We propose a new 3-component Degasperis–Procesi (3-DP) system. By investigating the bi-Hamiltonian structure of the corresponding hierarchy, we find that the Hamiltonian functionals of the 3-DP hierarchy are local in the negative direction and homogeneous in both directions. We show that the 3-DP system is related to the first negative flow in a modified Yajima–Oikawa hierarchy via a reciprocal transformation. With the help of this reciprocal transformation and a Darboux transformation of the associated 3-DP system, we construct a Bäcklund transformation for the 3-DP system. Furthermore, we present a short-wave model of the 3-DP system. •We propose a new 3-component Degasperis–Procesi system.•The 3-DP system is connected to a negative modified Yajima–Oikawa system.•We construct a Bäcklund transformation for the 3-DP system.•We present a short-wave model of the 3-DP system.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2023.133763