Inverse Dynamic Problem for the Dirac System on Finite Metric Tree Graphs and the Leaf Peeling Method

TL;DR

This paper addresses the inverse problem for Dirac systems on finite metric trees, aiming to recover topology, edge lengths, and potentials using the Leaf peeling method, and introduces a new algorithm for the forward problem.

Contribution

It introduces a novel approach combining the Leaf peeling method with a new dynamic algorithm for Dirac systems on finite metric graphs.

Findings

Successful recovery of tree topology and potentials

Development of a new dynamic algorithm for the forward problem

Application of the Leaf peeling method to Dirac systems

Abstract

In this paper, we consider the inverse dynamic problem for the Dirac system on finite metric tree graphs. Our main goal is to recover the topology (connectivity) of a tree, lengths of edges, and a matrix potential function on each edge. We use the dynamic response operator as our inverse data and apply the Leaf peeling method. In addition, we present a new dynamic algorithm to solve the forward problem for the Dirac system on general finite metric graphs.