Partial data inverse problems for the nonlinear magnetic Schr\"odinger equation

Abstract

In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the time-dependent linear coefficients, electric and magnetic potentials, and nonlinear coefficients, provided that the divergence of the magnetic potential is given. Additionally, we also investigate both the forward and inverse problems for the linear magnetic Schr\"odinger equation with a time-dependent leading term. In particular, all coefficients are uniquely recovered from boundary data.