This article is cited in 2 papers

Limit relation between Toda chains and the elliptic $SL(N,\mathbb C)$ top

G. Aminov<sup>ab

a</sup> Institute for Theoretical and Experimental Physics, Moscow, Russia
^b Moscow Institute for Physics and Technology, Moscow, Russia

Abstract: We study a limit relation between the elliptic $SL(N,\mathbb C)$ top and Toda chains. We show that in the case of the nonautonomous $SL(2,\mathbb C)$ 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 $SL(2,\mathbb C)$ top, which allows representing the equations of motion of the nonautonomous Toda chain as the equation for isomonodromic deformations.

Keywords: integrable system, nonautonomous system, Painlevé equation, Inozemtsev limit, topological structure of phase space.

Received: 16.05.2012

DOI: 10.4213/tmf8358

 English version: Theoretical and Mathematical Physics, 2012, 171:2, 575–588

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