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

Abstract

We study an inverse problem for a magnetic fractional Schrödinger equation with both a linear potential

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.