Geodesic
Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schr\"odinger problem and KPI equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 181-210

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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. 
@article{TMF_1992_93_2_a0,
     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},
     publisher = {mathdoc},
     volume = {93},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a0/}
}
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M. Boiti; F. Pempinelli; A. K. Pogrebkov; M. K. Polivanov. Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schr\"odinger 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/