Inverse Dynamic Problem for a 1-D Dirac System on Finite Metric Tree Graphs and a Leaf Peeling Algorithm

Abstract

In this paper, we consider the inverse dynamic problem for a one-dimensional 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 a Leaf peeling algorithm. In addition, we present a new dynamic algorithm to solve the forward problem for the 1-D Dirac system on general finite metric tree graphs.