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- W2022202781 abstract "This work studies the direct and inverse fixed energy scattering problem for the two-dimensional Schrödinger equation with a rather limited nonlinear index of refraction. In particular, using the Born approximation, we prove that all singularities of the unknown compactly supported potential belonging in L2(R2) 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∞(R2). The main achievement here is the computation of the Born approximation, which is carried out using the total variation regularization method. Numerical examples with noisy data are given to illustrate the effectiveness of the method." @default.
- W2022202781 created "2016-06-24" @default.
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- W2022202781 date "2015-06-23" @default.
- W2022202781 modified "2023-09-24" @default.
- W2022202781 title "Inverse fixed energy scattering problem for the two-dimensional nonlinear Schrödinger operator" @default.
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- W2022202781 doi "https://doi.org/10.1080/17415977.2015.1055263" @default.
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