Geodesic
Complex WKB method for difference equations in bounded domains
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 236-254 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 $h$. 
@article{ZNSL_2015_438_a14,
     author = {A. A. Fedotov and E. V. Tschetka},
     title = {Complex {WKB} method for difference equations in bounded domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {236--254},
     year = {2015},
     volume = {438},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a14/}
}
TY  - JOUR
AU  - A. A. Fedotov
AU  - E. V. Tschetka
TI  - Complex WKB method for difference equations in bounded domains
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 236
EP  - 254
VL  - 438
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a14/
LA  - ru
ID  - ZNSL_2015_438_a14
ER  - 
%0 Journal Article
%A A. A. Fedotov
%A E. V. Tschetka
%T Complex WKB method for difference equations in bounded domains
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 236-254
%V 438
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a14/
%G ru
%F ZNSL_2015_438_a14
A. A. Fedotov; E. V. Tschetka. Complex WKB method for difference equations in bounded domains. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 236-254. http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a14/

[1] V. Buslaev, A. Fedotov, “Kompleksnyi metod VKB dlya uravneniya Kharpera”, Algebra i Analiz, 6:3 (1994), 59–83 | MR

[2] M. V. Fedoryuk, Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Librokom, M., 2009

[3] A. Fedotov, F. Klopp, “A complex WKB method for adiabatic problems”, Asymptotic analysis, 27 (2001), 219–264 | MR | Zbl

[4] A. A. Fedotov, “Metod monodromizatsii v teorii pochti-periodicheskikh uravnenii”, Algebra i analiz, 25:2 (2013), 203–235 | MR