Drinfeld-sokolov hierarchies of type A and fourth order painlevé systems

Funkcialaj Ekvacioj

Volumn 53, Issue 1, 2010, Pages 143-167

  Fuji, Kenta ^a   Suzuki, Takao ^a  

^a KOBE UNIVERSITY   (Japan)

Author keywords

Affine Lie algebra; Integrable systems; Painlev equations

Indexed keywords

EID: 77953377698     PISSN: 05328721     EISSN: None     Source Type: Journal    
DOI: 10.1619/fesi.53.143     Document Type: Article

References (17)

1. Ablowitz, M. J. and Segur, H., Exact linearization of a Painlevé transcendent, Phys. Rev. Lett, 38 (1977), 1103-1106.
2. Carter, R., Conjugacy classes in the Weyl group, Compositio Math., 25 (1972), 1-59.
3. Delduc, F. and Fehér, L., Regular conjugacy classes in the Weyl group and integral hierarchies, J. Phys. A, 28 (1995), 5843-5882.
4. Drinfel'd, V. G. and Sokolov, V. V., Lie algebras and equations of Korteweg-de Vries type, J. Soviet Math., 30 (1985), 1975-2036.
5. 2n+2 arising from integrable hierarchy, Int. Math. Res. Not. IMRN, 2008 (2008), Art.IDrnml29, 21pp.
6. de Groot, M. F., Hollowood, T. J. and Miramontes, J. L., Generalized Drinfeld-Sokolov hierarchies, Comm. Math. Phys., 145 (1992), 57-84.
7. Iwasaki, K., Kimura, H., Shimomura, S. and Yoshida, M., From Gauss to Painlevé-A Modern Theory of Special Functions, Aspects of Mathematics El6, Vieweg, 1991.
8. Kac, V. G., Infinite dimensional Lie algebras, Cambridge University Press, 1990.
9. Kikuchi, T., Ikeda, T. and Kakei, S., Similarity reduction of the modified Yajima-Oikawa equation, J. Phys. A, 36 (2003), 11465-11480.
10. Kakei, S. and Kikuchi, T., Affine Lie group approach to a derivative nonlinear Schrödinger equation and its similarity reduction, Int. Math. Res. Not., 2004 (2004), 4181- 4209.
11. 3 hierarchy, Lett. Math. Phys., 79 (2007), 221-234.
12. 3, Comm. Math. Phys., 137 (1991), 67-107.
13. 8, in Symposium on Anomalies, Geometry and Topology (ed. W. A. Baedeen and A. R. White), World Scientific, 1985, 276-298.
14. l, Funkcial. Ekvac, 41 (1998), 483-503.
15. Noumi, M. and Yamada, Y., Birational Weyl group action arising from a nilpotent Poisson algebra, in Physics and Combinatorics 1999, Proceedings of the Nagoya 1999 International Workshop (ed. A. N. Kirillov, A. Tsuchiya and H. Umemura), World Scientific, 2001, 287-319.
16. Noumi, M. and Yamada, Y., A new Lax pair for the sixth Painlevé equation associated with sô(8), in Microlocal Analysis and Complex Fourier Analysis (ed. T. Kawai and K. Fujita), World Scientific, 2002, 238-252.
17. l, RIMS Koukyuroku No. 1473, (2006), 143-163.