Liouville Correspondences between Integrable Hierarchies
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 equati...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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Інститут математики НАН України
2017
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| Zitieren: | Liouville Correspondences between Integrable Hierarchies / J. Kang, X. Liu, P.J. Olver, C. Qu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 64 назв. — англ. |
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Kang, J. Liu, X. Olver, P.J. Qu, C. 2019-02-18T16:47:36Z 2019-02-18T16:47:36Z 2017 Liouville Correspondences between Integrable Hierarchies / J. Kang, X. Liu, P.J. Olver, C. Qu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 64 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K05; 37K10 DOI:10.3842/SIGMA.2017.035 https://nasplib.isofts.kiev.ua/handle/123456789/148632 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. The authors thank the referees for valuable comments and suggestions. Kang’s research was supported by NSFC under Grant 11631007 and Grant 11471260. Liu’s research was supported in part by NSFC under Grant 11631007 and Grant 11401471, and Ph.D. Programs Foundation of Ministry of Education of China-20136101120017. Olver’s research was supported by NSF under Grant DMS-1108894. Qu’s research was supported by NSFC under Grant 11631007 and Grant 1147117. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Liouville Correspondences between Integrable Hierarchies Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Liouville Correspondences between Integrable Hierarchies |
| spellingShingle |
Liouville Correspondences between Integrable Hierarchies Kang, J. Liu, X. Olver, P.J. Qu, C. |
| title_short |
Liouville Correspondences between Integrable Hierarchies |
| title_full |
Liouville Correspondences between Integrable Hierarchies |
| title_fullStr |
Liouville Correspondences between Integrable Hierarchies |
| title_full_unstemmed |
Liouville Correspondences between Integrable Hierarchies |
| title_sort |
liouville correspondences between integrable hierarchies |
| author |
Kang, J. Liu, X. Olver, P.J. Qu, C. |
| author_facet |
Kang, J. Liu, X. Olver, P.J. Qu, C. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148632 |
| citation_txt |
Liouville Correspondences between Integrable Hierarchies / J. Kang, X. Liu, P.J. Olver, C. Qu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 64 назв. — англ. |
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2025-12-07T19:56:56Z |
| last_indexed |
2025-12-07T19:56:56Z |
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