The Complex WKB Method for Difference Equations in Bounded Domains

The difference Schrӧdinger equation ψ(z+h)+ψ(zh)+v(z)ψ(z) = (z), z ∈ ℂ, is considered, where h > 0 and E ∈ ℂ are parameters and v is a function analytic in a bounded domain D ⊂ ℂ. An asymptotic method is developed for studying its solutions in the domain D for small positive h. Bibliography: 4 titles.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    V. Buslaev and A. Fedotov, “The complex WKB method for the Harper equation,” Algebra Analiz, 6, No. 3, 59–83 (1994).

  2. 2.

    M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations [in Russian], Librokom, Moscow (2009).

    Google Scholar 

  3. 3.

    A. Fedotov and F. Klopp, “A complex WKB method for adiabatic problems,” Asymptotic Analysis, 27, 219–264 (2001).

    MathSciNet  MATH  Google Scholar 

  4. 4.

    A. A. Fedotov, “The method of monodromization in the theory of quasiperiodic equations,” Algebra Analiz, 25, No. 2, 203–235 (2013).

Download references

Author information

Affiliations

Authors

Corresponding authors

Correspondence to A. A. Fedotov or E. V. Shchetka.

Additional information

Dedicated to Vasilii Mikhailovich Babich, brilliant scientist and remarkable person

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 438, 2015, pp. 236–256.

Translated by N. B. Lebedinskaya.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fedotov, A.A., Shchetka, E.V. The Complex WKB Method for Difference Equations in Bounded Domains. J Math Sci 224, 157–169 (2017). https://doi.org/10.1007/s10958-017-3402-8

Download citation