Liouville correspondences between multicomponent integrable hierarchies

Jing Kang, Xiaochuan Liu, P. J. Olver, Changzheng Qu

Research output: Contribution to journalArticlepeer-review

Abstract

Abstract: We establish Liouville correspondences for the integrable two-component Camassa–Holm hierarchy, the two-component Novikov (Geng–Xue) hierarchy, and the two-component dual dispersive water wave hierarchy using the related Liouville transformations. This extends previous results for scalar Camassa–Holm and KdV hierarchies and Novikov and Sawada–Kotera hierarchies to the multicomponent case.

Original languageEnglish (US)
Pages (from-to)843-874
Number of pages32
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume204
Issue number1
DOIs
StatePublished - Jul 1 2020

Bibliographical note

Funding Information:
The research of C. Qu was supported by the National Science Foundation of China (Grant Nos. 11631007 and 11971251).

Funding Information:
The research of J. Kang was supported by the National Science Foundation of China (Grant Nos. 11631007 and 11871395) and the National Science Basic Research Program of Shaanxi (No. 2019JC-28).

Funding Information:
The research of X. Liu was supported by the National Science Foundation of China (Grant Nos. 11722111 and 11631007).

Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • Liouville transformation
  • bi-Hamiltonian structure
  • two-component Camassa–Holm system
  • two-component Novikov system
  • two-component dual dispersive water wave system

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