Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 054, 11 pages      math-ph/0703072      http://dx.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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