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

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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},
     publisher = {mathdoc},
     volume = {438},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a14/}
}
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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/