Abstract:
Connections between Toda lattices (Toda chains) and similar
non-linear chains and the theory of orthogonal polynomials on the real axis have been
studied in detail during the last decades. Another system of difference
differential equations, known as the Schur flow, is considered in this paper
in the framework of the theory of orthogonal polynomials on the unit circle.
A Lax pair for this system is found and the dynamics of the corresponding
spectral measure is described. The general result is illustrated by
an example of Bessel modified measures on the unit circle: the large-time
asymptotic behaviour of their reflection coefficients is determined.
Bibliography: 23 titles.
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