Partial Data Inverse Problems for Nonlinear Magnetic Schr\'odinger Equations

We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $\mathbb{R}^n, n\geq2$, can uniquely determine, in a nonlinear magnetic Schr\"odinger equation, the vector-valued magnetic potential and the scalar electric potential, both being nonlinear in the solution.
Comment: 20 pages