Abstract
We introduce a linear problem with a spectral parameter for the elliptic form of the Painlevé VI equation. The corresponding nonautonomous version produces the Lax pair with spectral parameter for the Calogero-Inozemtsev model with a single degree of freedom.
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References
P. Painlevé: C. R. Acad. Sci. 143 (1906) 1111.
Yu.I. Manin: alg-geom/9605010; Amer. Math. Soc. Transl., Series 2, 186 (1998) 131.
A. Babich and L. Bordag: The elliptic form of the sixth Painlev´e equation, Preprint NTZ 25/1997.
B. Gambier: Acta Math. Ann. 33 (1910) 1.
R. Fuchs: Math. Annalen 63 (1907) 301.
L. Schlesinger: J. Reine Angew. Math. 141 (1912) 96.
D. Korotkin: math-ph/0003016.
A. Levin and M. Olshanetsky: Amer. Math. Soc. Transl., Series 2, 191 (1999).
I. Krichever: hep-th/0112096.
V.I. Inozemtsev: Lett. Math. Phys. 17 (1989) 11. F. Calogero: J. Math. Phys. 12 (1971) 419. J. Moser: Adv. Math. 16 (1975) 197.
A. Weyl: Elliptic functions according to Eisenstein and Kronecker, Springer-Verlag, Berlin–Heidelberg, 1976.
D. Mumford: Tata Lectures on Theta I., II., Birkhäuser, Boston, 1983, 1984. 1152 Czech. J. Phys. 53 (2003)
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Zotov, A. Elliptic Linear Problem for Painlevé VI Equation with Spectral Parameter. Czechoslovak Journal of Physics 53, 1147–1152 (2003). https://doi.org/10.1023/B:CJOP.0000010547.66922.21
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DOI: https://doi.org/10.1023/B:CJOP.0000010547.66922.21