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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 7
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Articles

WKB asymptotics of meromorphic solutions to difference equations

ORCID Icon &
Pages 1557-1573 | Received 19 Apr 2019, Accepted 26 Jul 2019, Published online: 16 Aug 2019
 

Abstract

We consider the difference Schrödinger equation ψ(z+h)+ψ(zh)+v(z)ψ(z)=Eψ(z) where z is a complex variable, E is a spectral parameter, and h is a small positive parameter. If the potential v is an analytic function, then, for h sufficiently small, the analytic solutions to this equation have standard semi-classical behavior that can be described by means of an analog of the complex WKB method for differential equations. We assume that v has a simple pole and, in its neighborhood, we study the asymptotics of meromorphic solutions to the difference Schrödinger equation.

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Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Alexander Fedotov  http://orcid.org/0000-0002-8010-3004

Additional information

Funding

The work was supported by PRC CNRS France, and the Russian Foundation for Basic Research under the grant No 17-51-150008.

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