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

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.