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Zap. Nauchn. Sem. POMI, 2015, Volume 438, Pages 236–254 (Mi znsl6194)  

This article is cited in 3 scientific papers (total in 3 papers)

Complex WKB method for difference equations in bounded domains

A. A. Fedotov, E. V. Tschetka

St. Petersburg State University, St. Petersburg, Russia

Abstract: We consider the difference Schrödinger equation $\psi(z+h)+\psi(z-h)+v(z)\psi(z)=E\psi(z)$, $z\in\mathbb C$, where $h>0$ and $E\in\mathbb C$ are parameters, and $v$ is a function analytic in a bounded domain $D\subset\mathbb C$. We develop an asymptotic method to study its solutons in the domain $D$ for small positive $h$.

Key words and phrases: difference Schrödinger equation, complex WKB method.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00165-a
Saint Petersburg State University 11.38.263.2014


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English version:
Journal of Mathematical Sciences (New York), 2017, 224:1, 157–169

Bibliographic databases:

UDC: 517
Received: 14.10.2015

Citation: A. A. Fedotov, E. V. Tschetka, “Complex WKB method for difference equations in bounded domains”, Mathematical problems in the theory of wave propagation. Part 45, Zap. Nauchn. Sem. POMI, 438, POMI, St. Petersburg, 2015, 236–254; J. Math. Sci. (N. Y.), 224:1 (2017), 157–169

Citation in format AMSBIB
\Bibitem{FedShc15}
\by A.~A.~Fedotov, E.~V.~Tschetka
\paper Complex WKB method for difference equations in bounded domains
\inbook Mathematical problems in the theory of wave propagation. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 438
\pages 236--254
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6194}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3501077}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 1
\pages 157--169
\crossref{https://doi.org/10.1007/s10958-017-3402-8}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fedotov A., Shchetka E., “Complex Wkb Method For Difference Equations in Unbounded Domains”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), eds. Motygin O., Kiselev A., Kapitanova P., Goray L., Kazakov A., Kirpichnikova A., IEEE, 2016, 140–143  crossref  isi  scopus
    2. A. A. Fedotov, E. V. Shchetka, “Complex WKB method for the difference Schrödinger equation with the potential being a trigonometric polynomial”, St. Petersburg Math. J., 29:2 (2018), 363–381  mathnet  crossref  isi  elib
    3. A. Fedotov, F. Klopp, “Difference equations, uniform quasiclassical asymptotics and Airy functions”, 2018 Days on Diffraction (DD), eds. O. Motygin, A. Kiselev, L. Goray, A. Kazakov, A. Kirpichnikova, M. Perel, IEEE, 2018, 98–101  crossref  isi
  • Записки научных семинаров ПОМИ
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