Inverse Scattering on Matrices with Boundary Conditions

TL;DR

This paper develops a method for inverse scattering of matrix Schrödinger operators with boundary conditions, enabling recovery of potentials and boundary conditions, applicable to star-shaped graphs.

Contribution

Introduces a Marchenko equation-based approach for inverse scattering with general boundary conditions, extending to star-shaped graph structures.

Findings

Successfully recovers potentials and boundary conditions

Applicable to star-shaped graph boundary problems

Extends inverse scattering theory to matrix operators

Abstract

We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary conditions. It is easily specialised to inverse scattering on star-shaped graphs with boundary conditions at the node.