Direct and inverse scattering on noncompact star-type quantum graph with Bessel singularity

TL;DR

This paper investigates inverse and direct scattering problems on a noncompact star-shaped quantum graph with Bessel-type singularities, providing uniqueness results and a constructive method for solving the inverse problem.

Contribution

It introduces a new approach to inverse scattering on star-type quantum graphs with Bessel singularities, including a uniqueness theorem and a constructive solution procedure.

Findings

Proved uniqueness of the inverse scattering problem.

Developed a constructive method for solving the inverse problem.

Analyzed the scattering on star-type quantum graphs with Bessel singularities.

Abstract

In this paper we study the noncompact star-type graph with perturbed radial Schrodinger equation on each ray and the matching conditions of some special form at the vertex. The results include the uniqueness theorem and constructive procedure for solution of the inverse scattering problem.