Evolution of Weyl functions and initial-boundary value problems

TL;DR

This paper reviews recent advances in Weyl theory, inverse problems, and their applications to integrable wave equations, focusing on initial-boundary value problems and reducing boundary conditions.

Contribution

It introduces new approaches to simplify overdetermined initial-boundary value problems and explores connections between dynamical and spectral systems.

Findings

Reduced the number of boundary conditions needed for certain problems

Established links between response and Weyl functions

Analyzed evolution of Weyl functions in integrable systems

Abstract

This review is dedicated to some recent results on Weyl theory, inverse problems, evolution of the Weyl functions and applications to integrable wave equations in a semistrip and quarter-plane. For overdetermined initial-boundary value problems, we consider some approaches, which help to reduce the number of the initial-boundary conditions. The interconnections between dynamical and spectral Dirac systems, between response and Weyl functions are studied as well.