Liouville Correspondences between Integrable Hierarchies
Exactly Solvable and Integrable Systems
2017-05-30 v2
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.
Keywords
Cite
@article{arxiv.1702.01227,
title = {Liouville Correspondences between Integrable Hierarchies},
author = {Jing Kang and Xiaochuan Liu and Peter J. Olver and Changzheng Qu},
journal= {arXiv preprint arXiv:1702.01227},
year = {2017}
}