Liouville Correspondences between Integrable Hierarchies

Symmetry Integrability and Geometry-Methods and Applications

article

Jing Kang¹  Xiaochuan Liu¹  Peter J. Olver²  Changzheng Qu³ 

[1] Center for Nonlinear Studies and School of Mathematics, Northwest University;School of Mathematics, University of Minnesota;Center for Nonlinear Studies and Department of Mathematics, Ningbo University

关键词: Liouville transformation;    Miura transformation;    bi-Hamiltonian structure;    conservation law;    Novikov equation;    Degasperis–Procesi equation;    Sawada–Kotera equation;    Kaup–Kupershmidt equation;   

DOI  :  10.3842/SIGMA.2017.035

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown