Geodesic
Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and KPI equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 181-210 
M. Boiti; F. Pempinelli; A. K. Pogrebkov; M. K. Polivanov. Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and KPI equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 181-210. http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a0/
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     author = {M. Boiti and F. Pempinelli and A. K. Pogrebkov and M. K. Polivanov},
     title = {Resolvent approach for two-dimensional scattering problems. {Application} to the nonstationary {Schr\"odinger} problem and {KPI} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {181--210},
     year = {1992},
     volume = {93},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The resolvent operator of the Linear Problem is determined as full Green function continued in the complex domain in two variables. An analog of the known Hilbert Identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the Nonstationary Schrödinger Equation as an example we show that all types of solutions of the Linear Problem as well as Spectral Data known in the literature are given as specific values of this unique function — resolvent. New form of Inverse Problem is formulated.

[1] Boiti M., Pempinelli F., Pogrebkov A. K., Polivanov M. K., “Resolvent approach for the nonstationary Schrödinger equation (standard case of rapidly decreasing potential”, Nonlinear evolution equations and dynamical systems (Baia Verde, 1991), World Sci. Publ., River Edge, NJ, 1992, 97–107 | MR | Zbl

[2] Boiti M., Pempinelli F., Pogrebkov A. K., Polivanov M. C., Inverse problems, 8 (1992), 331 | DOI | MR | Zbl

[3] Zakharov V. E., Manakov S. V., Sov. Sci. Rev.–Phys. Rev., 1 (1979), 133; Manakov S. V., Physica D, 3 (1981), 420 | DOI | MR | Zbl

[4] Fokas A. S., Ablowitz M. J., Stud. Appl. Math., 69 (1983), 211 | DOI | MR | Zbl

[5] Novikov S. P., Manakov S. V., Pitaevskii L. P., Zakharov V. E., Theory of Solitons. The method of Inverse Scattering, Plenum, New York, 1984 | MR | Zbl

[6] Boiti M., Leon J., Pempinelli F., Phys. Lett. A, 141 (1989), 96, 101 | DOI | MR

[7] Xin Zhou, Comm. Math. Phys., 128 (1990), 551 | DOI | MR | Zbl