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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 204, Number 1, Pages 10–45
DOI: https://doi.org/10.4213/tmf9845 (Mi tmf9845) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Liouville correspondences between multicomponent integrable hierarchies

Jing Kanga, X. Liub, P. J. Olverc, C. Qud

a Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi'an, China
b School of Mathematics and Statistics, Xi’an Jiaotong University, Xi'an, Shaanxi, China
c School of Mathematics, University of Minnesota, Minneapolis, USA
d Center for Nonlinear Studies and Department of Mathematics, Ningbo University, Ningbo, China
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DOI: https://doi.org/10.4213/tmf9845
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.
Keywords: Liouville transformation, bi-Hamiltonian structure, two-component Camassa–Holm system, two-component Novikov system, two-component dual dispersive water wave system.
Funding agency Grant number
National Natural Science Foundation of China 11631007
11871395
11722111
11971251
Shaanxi Province 2019JC-28
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). The research of X. Liu was supported by the National Science Foundation of China (Grant Nos. 11722111 and 11631007). The research of C. Qu was supported by the National Science Foundation of China (Grant Nos. 11631007 and 11971251).
Received: 04.11.2019
Revised: 26.02.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 204, Issue 1, Pages 843–874
DOI: https://doi.org/10.1134/S0040577920070028
Bibliographic databases:
Document Type: Article
MSC: 37K05, 37K10
Language: Russian
Citation: Jing Kang, X. Liu, P. J. Olver, C. Qu, “Liouville correspondences between multicomponent integrable hierarchies”, TMF, 204:1 (2020), 10–45; Theoret. and Math. Phys., 204:1 (2020), 843–874
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    1. N. Li, L. Wu, “Reciprocal transformations of generalized negative flows in integrable hierarchies”, J. Phys. A: Math. Theor., 55:43 (2022), 435201  crossref  mathscinet
    2. H. Lundmark, J. Szmigielski, “A view of the peakon world through the lens of approximation theory”, Physica D: Nonlinear Phenomena, 440 (2022), 133446  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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