This article is cited in 2 papers

Liouville correspondences between multicomponent integrable hierarchies

Jing Kang^a, X. Liu^b, P. J. Olver^c, C. Qu<sup>d

a</sup> 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

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.

MSC: 37K05, 37K10

Received: 04.11.2019
Revised: 26.02.2020

DOI: 10.4213/tmf9845

 English version: Theoretical and Mathematical Physics, 2020, 204:1, 843–874

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