Geodesic
Inverse scattering problem on the axis for the Schrödinger operator with triangular $2\times 2$ matrix potential. II. Addition of the discrete spectrum
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 2, pp. 176-195 Cet article a éte moissonné depuis la source Math-Net.Ru

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The theorem of the necessary and sufficient conditions for the solvability of ISP under consideration is proved. The method of addition of the discrete spectrum to the considered matrix not self-adjoint case is developed. 
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     title = {Inverse scattering problem on the axis for the {Schr\"odinger} operator with triangular $2\times 2$ matrix potential. {II.~Addition} of the discrete spectrum},
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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. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 2, pp. 176-195. http://geodesic.mathdoc.fr/item/JMAG_2007_3_2_a2/

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

[2] L. D. Faddeyev, “Inverse Scattering Problem in Quantum Theory, II”, Modern Probl. Math., 3, VINITI, Moscow, 1974, 93–180 (Russian)

[3] VSP, Zeist, 1987 | MR

[4] Gordon and Breach, New York–London, 1963 | Zbl | Zbl

[5] E. I. Bondarenko, F. S. Rofe-Beketov, “Inverse Scattering Problem on the Semi-Axis for a System with a Triangular Matrix Potential”, Mat. phys., anal., geom., 10 (2003), 412–424 (Russian) | MR | Zbl

[6] E. I. Zubkova, F. S. Rofe-Beketov, “Inverse Scattering Problem on the axis for the Schrödinger Operator with Triangular $2\times2$ Matrix Potential. I: Main Theorem”, J. Math. Phys., Anal., Geom., 3 (2007), 47–60 | MR | Zbl