Geodesic
Justification of the asymptotics of three one-dimensional short-range particles scattering problem solution for the processes $3\to2$
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 40-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present work is a continuation of the 3 body one-dimensional scattering problem in the presence of the bound states. Full description and justification of the generalized eigenfunction asymptotics in the case of the repulsive potentials have a simple geometric description. In the case of the presence of the bound states, additional terms appear in the eigenfunction asymptotics. In previous works during the analysis of Faddeev's equations in coordinate representation an operator of special form appeared which was connected to scattering amplitude and which did not have a simple description. In the current work, some properties of that operator are described. In particular, we derive the solvability of Faddeev's equations. 
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I. V. Baibulov. Justification of the asymptotics of three one-dimensional short-range particles scattering problem solution for the processes $3\to2$. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 40-47. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a3/

[1] I. V. Baibulov, A. M. Budylin, S. B. Levin, “Zadacha rasseyaniya trekh odnomernykh korotkodeistvuyuschikh kvantovykh chastits pri nalichii svyazannykh sostoyanii v parnykh podsistemakh. Koordinatnye asimptotiki yadra rezolventy i sobstvennykh funktsii absolyutno nepreryvnogo spektra”, Zap. nauchn. sem. POMI, 483, 2019, 5–18 | MR

[2] L. D. Faddeev, “Matematicheskie voprosy kvantovoi teorii rasseyaniya dlya sistemy trekh chastits”, Tr. MIAN SSSR, 69, 1963, 3–122

[3] I. V. Baibulov, A. M. Budylin, S. B. Levin, “On justification of the asymptotics of eigenfunctions of the absolutely continuous spectrum in the problem of three one-dimensional short-range quantum particles with repulsion”, J. Math. Sci., 238:5 (2019), 566–590 | DOI | MR | Zbl