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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2019, Volume 15, Number 2, Pages 225–238
DOI: https://doi.org/10.15407/mag15.02.225 (Mi jmag724) 		 
Inverse scattering problems with the potential known on an interior subinterval

Yongxia Guo, Guangsheng Wei

Shaanxi Normal University, School of Mathematics and Information Science, Xi'an 710062, PR China
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DOI: https://doi.org/10.15407/mag15.02.225
Abstract: The inverse scattering problem for one-dimensional Schrödinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely determined by the mixed scattering data consisting of the scattering matrix, known potential on a finite interval, and one nodal point on the known interval for each eigenfunction.
Key words and phrases: Schrödinger equation, inverse scattering problem, potential recovery with partial data.
Received: 14.06.2016
Revised: 15.05.2017
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Document Type: Article
MSC: 34A55, 34L25, 34L40.
Language: English
Citation: Yongxia Guo, Guangsheng Wei, “Inverse scattering problems with the potential known on an interior subinterval”, Zh. Mat. Fiz. Anal. Geom., 15:2 (2019), 225–238
Citation in format AMSBIB
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\by Yongxia~Guo, Guangsheng~Wei
\paper Inverse scattering problems with the potential known on an interior subinterval
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2019
\vol 15
\issue 2
\pages 225--238
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