Geodesic
Direct and Inverse Multichannel Scattering Problems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 58-77

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We consider small oscillations of a system of pairwise interacting particles in an external field near a stable equilibrium. The system is assumed to consist of finitely many channels, i.e., semi-infinite linear chains of particles, attached to a scatterer, which is a finite system of interacting particles. Direct and inverse scattering problems are considered. In particular, an algorithm finding characteristics of the channels on the basis of scattering data is given.
Keywords: inverse scattering problem, Sturm–Liouville operator, differential-difference operator
Mots-clés : Jacobi matrix. 
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     author = {Yu. I. Lyubarskii and V. A. Marchenko},
     title = {Direct and {Inverse} {Multichannel} {Scattering} {Problems}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a4/}
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Yu. I. Lyubarskii; V. A. Marchenko. Direct and Inverse Multichannel Scattering Problems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 2, pp. 58-77. http://geodesic.mathdoc.fr/item/FAA_2007_41_2_a4/