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 Keldysh Institute preprints, 2000, 012 (Mi ipmp1157)

The continuum limit of the Toda lattice and discrete orthogonal polynomials

A. I. Aptekarev, W. Van Assche, A. B. Kuijlaars

Abstract: A method for integration of the Cauchy problem for the hyperbolic system (the so-called continuum limit of the Toda lattice, see above) is proposed. ∂ α / ∂ t = - ($\beta$-α)/4 ∂ α/ ∂ x, ∂ $\beta$ / ∂ t = - ($\beta$-α)/4 ∂ $\beta$/ ∂ x, α(x,0)=α(x), $\beta$(x,0)=$\beta$(x), α(0,t)=$\beta$(0,t)=α(0), α(1,t)=$\beta$(1,t)=α(1). The method is based on some extremal problems of the theory of logarithmic potentials. The method is justified by means of the known results of the asymptotic theory of the polynomials orthogonal with respect to a discrete measure.

Full text: http:/.../preprint.asp?id=2000-12&lg=r

Citation: A. I. Aptekarev, W. Van Assche, A. B. Kuijlaars, “The continuum limit of the Toda lattice and discrete orthogonal polynomials”, Keldysh Institute preprints, 2000, 012

Citation in format AMSBIB
\Bibitem{AptVanKui00} \by A.~I.~Aptekarev, W.~Van Assche, A.~B.~Kuijlaars \paper The continuum limit of the Toda lattice and discrete orthogonal polynomials \jour Keldysh Institute preprints \yr 2000 \papernumber 012 \mathnet{http://mi.mathnet.ru/ipmp1157} 

• http://mi.mathnet.ru/eng/ipmp1157
• http://mi.mathnet.ru/eng/ipmp/y2000/p12

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This publication is cited in the following articles:
1. M. A. Lapik, “Ekstremalnaya mera i vneshnee pole v dvuparametricheskikh vektornykh zadachakh ravnovesiya logarifmicheskogo potentsiala”, Preprinty IPM im. M. V. Keldysha, 2016, 115, 20 pp.