B\"acklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem

TL;DR

This paper develops a GBDT-based Backlund-Darboux transformation for non-isospectral canonical systems, crucial in random matrix theory, and addresses the associated Riemann-Hilbert problem with explicit formulas and solutions.

Contribution

It introduces a novel GBDT approach for non-isospectral systems and provides explicit solutions to the related Riemann-Hilbert problem.

Findings

Constructed GBDT version of Backlund-Darboux transformation

Solved the Riemann-Hilbert problem explicitly

Formulated and solved the inverse problem

Abstract

A GBDT version of the Backlund-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.