Toda chain,Stieltjes function,and orthogonal polynomials |
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| Authors: | F Peherstorfer V P Spiridonov A S Zhedanov |
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| Institution: | (1) Institut für Analysis und Numerik, Johannes Kepler Universitat Linz, A-4040 Linz, Austria;(2) Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia;(3) Donetsk Institute for Physics and Technology, Donetsk, Ukraine |
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| Abstract: | We discuss relations between the theory of orthogonal polynomials, Hankel determinants, and the unrestricted one-dimensional
Toda chain. In particular, we show that the equations of motion for the Toda chain are equivalent to a Riccati equation for
the Stieltjes function. We consider some examples of the Stieltjes function with an explicit (hypergeometric and elliptic)
time dependence in detail.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 81–108, April, 2007. |
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| Keywords: | integrable system Toda chain orthogonal polynomial |
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