Inverse Scattering Problem for a Piecewise Continuous Sturm - Liouville Equation with Eigenparameter Dependence in the Boundary Conditon

TL;DR

This paper investigates the inverse scattering problem for a piecewise continuous Sturm-Liouville equation with eigenparameter-dependent boundary conditions, establishing properties of scattering data and a uniqueness algorithm for potential recovery.

Contribution

It introduces a new inverse scattering framework for piecewise continuous Sturm-Liouville equations with quadratic eigenparameter dependence in boundary conditions, including a uniqueness algorithm.

Findings

Defined scattering data for the problem

Investigated properties of the scattering data

Developed a uniqueness algorithm for potential reconstruction

Abstract

In this study, the inverse problem of the scattering theory on the half line for a piecewise continuous Sturm-Liouville equation with boundary condition depending quadratic on the spectral parameter is considered. The scattering data of the problem is defined, some properties of the scattering data are investigated. The main equation is derived and uniqueness algorithm to the potential with given scattering data is studied.