The heun equation and the calogero-moser-sutherland system IV: The Hermite-Krichever Ansatz

Communications in Mathematical Physics

Volumn 258, Issue 2, 2005, Pages 367-403

  Takemura, Kouichi ^a  

^a YOKOHAMA CITY UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22544439074     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1359-9     Document Type: Article

References (16)

1. Belokolos, E.D.,Knolskii, V.Z.: Reduction of Abelian functions and algebraically integrable systems. II. J. Math. Sci. (New York) 108, 295-374 (2002)
2. Gesztesy, F.,Weikard, R.: Treibich-Verdier potentials and the stationary (m)KdV hierarchy. Math. Z. 219, 451-476 (1995)
3. Hermite, C.: Oeuvres de Charles Hermite, Vol. III. Paris: Gauthier-Villars, 1912
4. Inozemtsev, V.I.: Lax representation with spectral parameter on a torus for integrable particle systems. Lett. Math. Phys. 17, 11-17 (1989)
5. Krichever, I.M.: Elliptic solutions of the Kadomeev-Petviasvili equations, and integrable systems of particles. Fund. Anal. Appl. 14, 282-290 (1980)
6. Maier, R.S.: Lamé polynomials, hyperelliptic reductions and Lamé band structure. http://www.arxiv.org/abs/math-ph/0309005v1, 2003
7. Ochiai, H.,Oshima, T.,Sekiguchi, H.: Commuting families of symmetric differential operators. Proc. Japan. Acad. 70, 62-66 (1994)
8. Ronveaux, A.(ed.): Heun's differential differential equations. Oxford Science Publications. Oxford: Oxford University Press 1995
9. Smirnov, A.O.: Elliptic solutions of the Korteweg-de Vries equation. Math. Notes 45, 476-481 (1989)
10. Smirnov, A.O.: Finite-gap elliptic solutions of the KdV equation. Acta Appl. Math. 36, 125-166 (1994)
11. Smirnov, A.O.: Elliptic solitons and Heun's equation. In: The Kowalevski property, CRM Proc. Lecture Notes 32, Providence, RI: Amer. Math. Soc.,2002, pp. 287-305
12. Takemura, K.: The Heun equation and the Calogero-Moser-Sutherland system I: the Bethe Ansatz method. Commun. Math. Phys. 235, 467-494 (2003)
13. Takemura, K.: The Heun equation and the Calogero-Moser-Sutherland system II: the perturbation and the algebraic solution. Electron. J. Differ. Eqs. 2004(15), 1-30 (2004)
14. Takemura, K.: The Heun equation and the Calogero-Moser-Sutherland system III: the finite gap property and the monodromy. J. Nonlinear Math. Phys. 11, 21-46 (2004)
15. Treibich, A.,Verdier, J.-L.: Revetements exceptionnels et sommes de 4 nombres triangulaires (French). Duke Math. J. 68, 217-236 (1992)
16. Weikard, R.: On Hill's equation with a singular complex-valued potential. Proc. London Math. Soc. 3, 76, 603-633 (1998)