Dichotomy of WKB-Solutions of Discrete Schrödinger Equation

Authors:
S. A. Stepin;V. A. Titov
Affiliations:
Moscow State University and University in Bialystok, Information not available, Information not available Information not available;Moscow State University, Information not available, Information not available Information not available
Venue:
Journal of Dynamical and Control Systems
Year:
2006

Citing 2
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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.