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arXiv · 1404.6910

Inverse fixed energy scattering problem for the two-dimensional nonlinear Schroedinger operator

Georgios Fotopoulos·Valery Serov
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Abstract

This work studies the direct and inverse fixed energy scattering problem for two-dimensional Schroedinger equation with rather general nonlinear index of refraction. In particular, using the Born approximation we prove that all singularities of the unknown compactly supported potential from $L^2$-space can be obtained uniquely by the scattering data with fixed positive energy. The proof is based on the new estimates for the Faddeev-Green's function in $L^\infty$-space.

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Georgios Fotopoulos, Valery Serov. 2014-12-01. Inverse fixed energy scattering problem for the two-dimensional nonlinear Schroedinger operator. https://arxiv.org/abs/1404.6910

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