On an inverse dynamic problem for the wave equation with a potential on a real line

TL;DR

This paper investigates an inverse problem for the wave equation with a potential on a real line, utilizing boundary triplets and a response operator to connect dynamic and spectral inverse problems.

Contribution

It introduces a novel approach to formulate the inverse problem using boundary triplets and links it to spectral inverse problems via matrix-valued measures.

Findings

Derived equations for the inverse problem.

Established relationship between dynamic and spectral inverse problems.

Proposed a framework for solving inverse problems with boundary triplets.

Abstract

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator (dynamic Dirichlet-to-Neumann map). We derive equations of inverse problem and also point out the relationship between dynamic inverse problem and spectral inverse problem from a matrix-valued measure.