Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds

Abstract

We study the inverse boundary problem for a nonlinear magnetic Schrodinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the knowledge of the Dirichlet-to-Neumann map on the boundary of the manifold determines the nonlinear magnetic and electric potentials uniquely. No assumptions on the transversal manifold are made in this result, whereas the corresponding inverse boundary problem for the linear magnetic Schrodinger operator is still open in this generality.