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 language||English (US)|
|Number of pages||32|
|Journal||Theoretical and Mathematical Physics(Russian Federation)|
|State||Published - Jul 1 2020|
Bibliographical noteFunding Information:
The research of C. Qu was supported by the National Science Foundation of China (Grant Nos. 11631007 and 11971251).
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).
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- Liouville transformation
- bi-Hamiltonian structure
- two-component Camassa–Holm system
- two-component Novikov system
- two-component dual dispersive water wave system