Geodesic
Necessary and sufficient conditions in inverse scattering problem on the axis for the triangular $2\times 2$ matrix potential
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009) no. 3, pp. 296-309 Cet article a éte moissonné depuis la source Math-Net.Ru

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The characteristic properties of the scattering data for the Schrödinger operator on the axis with a triangular $2\times 2$ matrix potential are obtained. A difference between the necessary and sufficient conditions for solvability of ISP under consideration, contained in the previous works of the authors, is eliminated. 
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E. I. Zubkova; F. S. Rofe-Beketov. Necessary and sufficient conditions in inverse scattering problem on the axis for the triangular $2\times 2$ matrix potential. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009) no. 3, pp. 296-309. http://geodesic.mathdoc.fr/item/JMAG_2009_5_3_a3/

[1] Birkhäuser, Basel, 1986 | MR | Zbl

[2] J. Soviet Math., 5 (1976), 334–396 | DOI | MR | Zbl

[3] VSP, Zeist, 1987 | MR

[4] E. I. Zubkova, F. S. Rofe-Beketov, “Inverse Scattering Problem on the Axis for the Schrödinger Operator with Triangular $2\times 2$ Matrix Potential. I. Main Theorem”, J. Math. Phys., Anal., Geom., 3:1 (2007), 47–60 | MR | Zbl

[5] E. I. Zubkova, F. S. Rofe-Beketov, “Inverse Scattering Problem on the Axis for the Schrödinger Operator with Triangular $2\times 2$ Matrix Potential. II. Addition of the Discrete Spectrum”, J. Math. Phys., Anal., Geom., 3:2 (2007), 176–195 | MR | Zbl

[6] V. E. Lyantse, “Nonselfadjoint Second Order Differential Operator on the Semiaxis”, Addendum I to the book: M. A. Naimark, Linear differential operators, 2nd Ed., Nauka, Moscow, 1969 (Russian) | Zbl

[7] I. P. Syroyid, The Composite Method of Inverse Scattering Problem and Studying Nonselfadjoint Lax Pairs for Korteveg-de Vries Systems, Ya.S. Pidstrygach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian National Acad. Sci., Lviv, 2005 (Ukrainian)

[8] F. D. Gakhov, Boundary Problems, Fizmatgiz, Moscow, 1958 (Russian)

[9] N. I. Muskhelishvili, Singular Integral Equations, Fizmatgiz, Moscow, 1962 (Russian)

[10] F. D. Gakhov, Yu. I. Cherskiy, Convolution Type Equations, Nauka, Moscow, 1978 (Russian) | Zbl