Geodesic
Inverse scattering on the half line for the matrix Schrödinger equation
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 3, pp. 237-269 Cet article a éte moissonné depuis la source Math-Net.Ru

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The matrix Schrödinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix potential is integrable, is selfadjoint, and has a finite first moment. The corresponding scattering data set is constructed, and such scattering data sets are characterized by providing a set of necessary and sufficient conditions assuring the existence and uniqueness of the one-to-one correspondence between the scattering data set and the input data set containing the potential and boundary matrices. The work presented here provides a generalization of the classic result by Agranovich and Marchenko from the Dirichlet boundary condition to the general selfadjoint boundary condition. 
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Tuncay Aktosun; Ricardo Weder. Inverse scattering on the half line for the matrix Schrödinger equation. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 3, pp. 237-269. http://geodesic.mathdoc.fr/item/JMAG_2018_14_3_a0/

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