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SIGMA 3 (2007), 054, 11 pages math-ph/0703072
https://doi.org/10.3842/SIGMA.2007.054
Contribution to the Vadim Kuznetsov Memorial Issue
Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem
Alexander Sakhnovich
Fakultät für Mathematik, Universität Wien,
Nordbergstrasse 15, A-1090 Wien, Austria
Received October 25, 2006, in final form March 19, 2007; Published online March 25, 2007
Abstract
A GBDT version of the Bäcklund-Darboux
transformation is constructed for a non-isospectral canonical
system, which plays essential role in the theory of random matrix
models. The corresponding Riemann-Hilbert problem is treated and
some explicit formulas are obtained. A related inverse problem is
formulated and solved.
Key words:
Bäcklund-Darboux transformation; canonical system; random matrix theory.
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