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Aoki, Takashi; Kawai, Takahiro; Koike, Tatsuya; Takei, Yoshitsugu

On the exact WKB analysis of microdifferential operators of WKB type. (English) Zbl 1079.34070

Ann. Inst. Fourier 54, No. 5, 1393-1421 (2004).
The paper is devoted to the introduction of a new class of integral operators, the so-called microdifferential operators of WKB type appearing in the plasma wave propagation in inhomogeneous media. The well-known results for differential operators of WKB analysis are extended to this new class with respect to exact WKB analysis based on Borel resummation. The development of the exact WKB analysis of microdifferential equations near their turning points is a consequence of the proof of a Weierstrass-type division theorem for microdifferential operators of WKB type.
Reviewer: J. Saurer (Regensburg)

Cited in 5 Documents

MSC:

34M60 Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs

Keywords:

exact WKB analysis; microdifferential operators of WKB type; turning points; Weierstrass-type division theorem for microdifferential operators; Berk-Book equation
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References:

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