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

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.