Inverse dynamic problem for the wave equation with periodic boundary conditions

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0 , 2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As inverse data we use a response operator (dynamic Dirichlet-to-Neumann map). Using the auxiliary problem on the whole line, we derive equations of the inverse problem. We also establish the relationships between dynamic and spectral inverse data.