An inverse problem for the magnetic fractional Schrödinger equation with nonlinear potential

We study an inverse problem for a magnetic fractional Schrödinger equation with both a linear potential q ( x ) $q(x)$ q left parenthesis x right parenthesis and a nonlinear potential a ( x , u ) $a(x,u)$ a left parenthesis x comma u right parenthesis analytic in u . The magnetic potential A ( x ) $A(x)$ upper A left parenthesis x right parenthesis is assumed to be known. We show that the exterior Dirichlet-to-Neumann map uniquely determines both the linear potential q and the full nonlinearity a . The proof relies on higher-order linearization and the Runge approximation property for the magnetic fractional Laplacian. Our work extends the linear magnetic Calderón problem to the nonlinear setting and provides a uniqueness result for recovering multiple unknown coefficients simultaneously.