Determination of Schrödinger nonlinearities from the scattering map
Rowan Killip, Jason Murphy, Monica Visan
Published: 2024/2/5
Abstract
We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schr\"odinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schr\"odinger solutions. We then solve this deconvolution problem using the Beurling--Lax Theorem.