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arXiv · 2402.03218

Determination of Schr\"odinger nonlinearities from the scattering map

Rowan Killip·Jason Murphy·Monica Visan
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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.

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Rowan Killip, Jason Murphy, Monica Visan. 2024-02-05. Determination of Schr\"odinger nonlinearities from the scattering map. https://arxiv.org/abs/2402.03218

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