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arXiv · 1702.01227

Liouville Correspondences between Integrable Hierarchies

Jing Kang·Xiaochuan Liu·Peter J. Olver·Changzheng Qu
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Abstract

In this paper, we study explicit correspondences between the integrable Novikov and Sawada-Kotera hierarchies, and between the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada-Kotera equations, and the isospectral problems of the Degasperis-Procesi and Kaup-Kupershmidt equations relate the corresponding hierarchies, in both positive and negative directions, as well as their associated conservation laws. Combining these results with the Miura transformation relating the Sawada-Kotera and Kaup-Kupershmidt equations, we further construct an implicit relationship which associates the Novikov and Degasperis-Procesi equations.

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Jing Kang, Xiaochuan Liu, Peter J. Olver, Changzheng Qu. 2017-02-04. Liouville Correspondences between Integrable Hierarchies. https://doi.org/10.3842/sigma.2017.035

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