Abstract: We consider an inverse problem of recovering a potential from the Dirichlet to Neumann map associated to a high-frequency linear Schrodinger equation on certain Riemannian manifolds. Here we extend some of the previous works to the case of simple manifolds, and more generally to manifolds, where the geodesic ray transform is stably invertible. We also discuss a similar problem corresponding to a nonlinear Schrodinger equation at fixed high frequency.
