The Complex WKB Method for Difference Equations and Airy Functions

DOI10.1137/18M1228694zbMath1425.39011arXiv1810.04918OpenAlexW2985315974WikidataQ126863523 ScholiaQ126863523MaRDI QIDQ5243248

Alexander Fedotov, Frédéric Klopp

Publication date: 18 November 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04918

zbMATH Keywords

difference equationsturning pointWKB method

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Difference equations in the complex domain (39A45)

Related Items (7)

Complex WKB method for a system of two linear difference equations ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ Semiclassical asymptotics of transition matrices for difference equations with two coalescing turning points ⋮ On the hierarchical behavior of solutions of the Maryland equation in the semiclassical approximation ⋮ Semiclassical asymptotics for a difference Schrödinger equation with two coalescent turning points ⋮ WKB asymptotics of meromorphic solutions to difference equations ⋮ Difference equations in the complex plane: quasiclassical asymptotics and Berry phase

Cites Work

• Lagrangian manifolds related to the asymptotics of Hermite polynomials
• Asymptotic expansions for second-order linear difference equations with a turning point
• The complex WKB method for difference equations in bounded domains
• Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
• The Ten Martini problem
• Asymptotic Approximations of Integrals
• Monodromization method in the theory of almost-periodic equations
• A solution procedure for second–order difference equations and its application to electromagnetic–wave diffraction in a wedge–shaped region
• Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
• Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial
• Rigorous WKB for Finite-Order Linear Recurrence Relations with Smooth Coefficients
• Unitary reduction for the two‐dimensional Schrödinger operator with strong magnetic field
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