Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem

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.