Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions

TL;DR

This paper introduces auxiliary systems for matrix nonisospectral equations, such as coupled NLS and KdV with variable coefficients, and constructs explicit solutions using the GBDT Bäcklund-Darboux transformation.

Contribution

It presents a novel approach to solving nonisospectral equations with external potentials via the GBDT method, expanding solution techniques for these complex systems.

Findings

Explicit solutions for nonisospectral equations were constructed.

Auxiliary systems for matrix nonisospectral equations were introduced.

The GBDT method was effectively applied to obtain solutions.

Abstract

Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of nonisospectral equations were constructed using the GBDT version of the B\"acklund-Darboux transformation.