Recovery of Schr\"odinger nonlinearity from the large-data scattering behavior

Yi Sun

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arXiv · 2607.14080

Recovery of Schr\"odinger nonlinearity from the large-data scattering behavior

Yi Sun

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Abstract

In this article, we study scattering and inverse scattering problems for 3D nonlinear Schr\"odinger equations of the form, $$ \mathrm{i}\partial_t u + \Delta u = a(x)|u|^2u.$$ For $a(x)$ in a suitable class, such equations are globally well-posed and admit a large-data scattering theory. In this work, we prove that the large-data scattering behavior uniquely determines the inhomogeneity $a(x)$.

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Yi Sun. 2026-07-15. Recovery of Schr\"odinger nonlinearity from the large-data scattering behavior. https://arxiv.org/abs/2607.14080

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