Liouville Correspondences between Integrable Hierarchies

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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dc.contributor.author	Kang, J.
dc.contributor.author	Liu, X.
dc.contributor.author	Olver, P.J.
dc.contributor.author	Qu, C.
dc.date.accessioned	2019-02-18T16:47:36Z
dc.date.available	2019-02-18T16:47:36Z
dc.date.issued	2017
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 37K05; 37K10
dc.identifier.other	DOI:10.3842/SIGMA.2017.035
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148632
dc.description.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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Liouville Correspondences between Integrable Hierarchies	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA