# Continuous and discrete dynamical Schr\"odinger systems: explicit solutions

## TL;DR

This paper develops explicit solutions for continuous and discrete dynamical Schr"odinger systems with matrix potentials using a generalized Bäcklund-Darboux transformation, and explores their asymptotic behavior over time.

## Contribution

It introduces a generalized Bäcklund-Darboux transformation method to construct explicit solutions for dynamical Schr"odinger systems with matrix potentials.

## Key findings

- Constructed explicit solutions for dynamical Schr"odinger systems.
- Analyzed asymptotic expansions of solutions in time.
- Extended the Bäcklund-Darboux transformation to a generalized form.

## Abstract

We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our generalized (GBDT) version of the B\"acklund-Darboux transformation. Asymptotic expansions of these solutions in time are of interest.