Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds

Abstract

We consider the problem of recovering a nonlinear potential function in a nonlinear Schrödinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex geometric optics solutions according to the wavenumber, we prove the increasing stability of recovering the coefficient of a cubic term as the wavenumber becomes large.