Liouville correspondences between multi-component integrable hierarchies
Jing Kang, Xiaochuan Liu, Peter J. Olver, and Changzheng Qu
TL;DR
This paper extends the concept of Liouville correspondences to multi-component integrable hierarchies, establishing transformations that connect different complex systems in mathematical physics.
Contribution
It introduces Liouville correspondences for multi-component integrable hierarchies, expanding previous scalar results to more complex multi-component systems.
Findings
Established Liouville correspondences for three multi-component hierarchies
Extended scalar hierarchy results to multi-component cases
Provided transformations linking different integrable systems
Abstract
In this paper, 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 by means of the related Liouville transformations. This extends previous results on the scalar Camassa-Holm and KdV hierarchies, and the Novikov and Sawada-Kotera hierarchies to the multi-component case.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Nonlinear Photonic Systems