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Dichotomy of WKB-Solutions of Discrete Schrödinger Equation

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Abstract

The asymptotic behavior of solutions of a discrete Schrödinger equation is studied via the perturbation theory approach and by the method based on the reduction to the Riccati equation. Solutions of WKB type are constructed which exhibit a dichotomy property similar to that known for differential equations. Provided that the potential is regularly varying in a certain sense, these solutions can be asymptotically represented as products of continued fraction approximants related to the corresponding Riccati equation.

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Authors and Affiliations

  1. Moscow State University and University in Bialystok, Information not available, Information not available, Information not available, Information not available, Information not available, Information not available

    S. A. Stepin

  2. Moscow State University, Information not available, Information not available, Information not available, Information not available, Information not available, Information not available

    V. A. Titov

Authors
  1. S. A. Stepin
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  2. V. A. Titov
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Corresponding authors

Correspondence to S. A. Stepin or V. A. Titov.

Additional information

2000 Mathematics Subject Classification. 34D09, 39A11, 39A12.

The work was supported by the Ministry for Science and Technology of Russia (project Nos. NSh-680.2003.1 and MD-251.2003.01).

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Stepin, S., Titov, V. Dichotomy of WKB-Solutions of Discrete Schrödinger Equation. J Dyn Control Syst 12, 135–144 (2006). https://doi.org/10.1007/s10450-006-9688-3

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  • DOI: https://doi.org/10.1007/s10450-006-9688-3

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