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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 251, Pages 10–53
(Mi tm44)
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This article is cited in 2 scientific papers (total in 2 papers)
Spectral Theory of the Nonstationary Schrödinger Equation with a Bidimensionally Perturbed One-Dimensional Potential
M. Boitia, F. Pempinellia, A. K. Pogrebkovb, B. Prinari a Lecce University
b Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We derive and describe in detail the extension of the inverse scattering transform method to the case of linear spectral problems with potentials that do not decay in some space directions. Our presentation is based on the extended resolvent approach. As a basic example, we consider the nonstationary Schrödinger equation with a potential that is a perturbation of a generic one-dimensional potential by means of a decaying function of two variables. We give the corresponding modifications of the Jost solutions and the spectral data and derive their properties and characterization equations.
Received in January 2005
Citation:
M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrödinger Equation with a Bidimensionally Perturbed One-Dimensional Potential”, Nonlinear dynamics, Collected papers, Trudy Mat. Inst. Steklova, 251, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 10–53; Proc. Steklov Inst. Math., 251 (2005), 6–48
Linking options:
https://www.mathnet.ru/eng/tm44 https://www.mathnet.ru/eng/tm/v251/p10
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Abstract page: | 582 | Full-text PDF : | 131 | References: | 58 |
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