Inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree

TL;DR

This paper addresses inverse problems for a one-dimensional Dirac system on a finite tree, aiming to recover the tree's structure and potentials using spectral and dynamic data.

Contribution

It introduces methods to reconstruct the topology and matrix potentials of a finite tree from spectral and dynamic response data for the Dirac system.

Findings

Successful reconstruction of tree topology and edge potentials.

Development of inverse problem algorithms for Dirac systems on trees.

Enhanced understanding of spectral and dynamic data roles in inverse problems.

Abstract

We consider inverse dynamic and spectral problems for the one dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity of edges) as well as matrix potentials on each edge. As inverse data we use the Weyl-Titchmarsh matrix function or the dynamic response operator.