Dynamical canonical systems and their explicit solutions

TL;DR

This paper explores dynamical canonical systems, establishing their connection with classical spectral systems, and provides explicit solutions via Bäcklund-Darboux transformations, with implications for evolution and control theories.

Contribution

It introduces explicit solutions for dynamical canonical systems using Bäcklund-Darboux transformations, linking them to classical spectral systems.

Findings

Explicit solutions constructed for dynamical canonical systems

Connections established with classical spectral systems

Properties of solutions relevant to evolution and control theories

Abstract

Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those properties of the solutions, which are of interest in evolution and control theories.