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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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Liouville Correspondences between Integrable Hierarchies
Інший ID:
2010 Mathematics Subject Classification: 37K05; 37K10
DOI:10.3842/SIGMA.2017.035
DOI:10.3842/SIGMA.2017.035
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
479
Завантажень:
266
Анотація:
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.
