Abstract
We study a limit relation between the elliptic SL(N,ℂ) top and Toda chains. We show that in the case of the nonautonomous SL(2, ℂ) top, whose equations of motion are related to the Painlevé VI equation, it turns out to be possible to modify the previously proposed procedure and in the limit obtain the nonautonomous Toda chain, whose equations of motion are equivalent to a particular case of the Painlevé III equation. We obtain the limit of the Lax pair for the elliptic SL(2, ℂ) top, which allows representing the equations of motion of the nonautonomous Toda chain as the equation for isomonodromic deformations.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 171, No. 2, pp. 179–195, May, 2012.
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Aminov, G.A. Limit relation between toda chains and the elliptic SL(N, ℂ) top. Theor Math Phys 171, 575–588 (2012). https://doi.org/10.1007/s11232-012-0056-z
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DOI: https://doi.org/10.1007/s11232-012-0056-z