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