Symmetries in the fourth painlevé equation and okamoto polynomials

Nagoya Mathematical Journal

Volumn 153, Issue , 1999, Pages 53-86

  Noumi, Masatoshi ^a   Yamada, Yasuhiko ^b  

^a KOBE UNIVERSITY   (Japan)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002515824     PISSN: 00277630     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0027763000006899     Document Type: Article

References (10)

1. S. Fukutani, K. Okamoto and H. Umemura, Special polynomials associated with the rational solutions and the Hirota bilinear relations of the 2nd and the 4th Painlevé equations, preprint.
2. M. Jimbo and T. Miwa, Solitons and infinite dimensional Lie algebras, Publ. RIMS, Kyoto Univ., 19 (1983), 943-1001.
3. M. Kac and P. van Moerbeke, On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices, Advances Math., 16 (1975), 160-169.
4. Y. Murata, Rational solutions of the second and the fourth equations of Painlevé. Funkcialaj Ekvacioj, 28 (1985), 1-32.
5. T. Nishitani and M. Tajiri, On similarity solutions of Boussinesq equation, Phys. Lett., 89A (1982), 379-380.
6. M. Noumi and K. Okamoto, Irreducibility of the second and the fourth Painlevé equations, Funkcialaj Ekvacioj, 40 (1997), 139-163.
7. IV, Math. Ann., 275 (1986), 221-255.
8. K. Okamoto, Algebraic relations among six adjacent τ-functions related to the fourth Painlevé system, Kyushu J. Math., 50 (1996), 513-532.
9. H. Umemura, On the irreducibility of the first differential equations of Painlevé.
10. G.R.W. Quispel, F. W. Nijhoff and H. W. Capel, Linearization of the Boussinesq equation and the modified Boussinesq equation, Phys. Lett., 91A (1982), 143-145.