Novikov, R. G. Approximate inverse quantum scattering at fixed energy in dimension 2. (English. Russian original) Zbl 0980.81058 Bukhshtaber, V. M. (ed.) et al., Solitons, geometry, and topology: on the crossroads. Collected papers dedicated to the 60th birthday of Academician Sergei Petrovich Novikov. Transl. from the Russian. Moscow: MAIK Nauka/Interperiodica, Proc. Steklov Inst. Math. 225, 285-302 (1999); translation from Tr. Mat. Inst. Steklova 225, 301-318 (1999). Summary: For the Schrödinger equation in dimension 2 we reconstruct the potential \(v\in W_\varepsilon^{N,1}(\mathbb{R}^2)\), \(\mathbb{N}\ni N\geq 3\), \(\varepsilon>0\) (\(N\)-times smooth potential) from the scattering amplitude \(f\) at fixed energy \(E\) up to \(O(E^{-(N-2)/2})\) in the uniform norm as \(E\to +\infty\).For the entire collection see [Zbl 0967.00102]. Cited in 10 Documents MSC: 81U40 Inverse scattering problems in quantum theory 34A55 Inverse problems involving ordinary differential equations 35P25 Scattering theory for PDEs Keywords:\(N\)-times smooth potential; Schrödinger equation; dimension 2; scattering amplitude PDFBibTeX XMLCite \textit{R. G. Novikov}, in: Solitons, geometry, and topology: on the crossroads. Collected papers dedicated to the 60th birthday of Academician Sergei Petrovich Novikov. Transl. from the Russian. Moscow: MAIK Nauka/In\-ter\-pe\-ri\-o\-di\-ca. 285--302 (1999; Zbl 0980.81058); translation from Tr. Mat. Inst. Steklova 225, 301--318 (1999)