# On the exact WKB analysis of microdifferential operators of WKB type

Takashi Aoki^{[1]}; Takahiro Kawai; Tatsuya Koike; Yoshitsugu Takei

- [1] Kinki University, School of Science and Engineering, Department of Mathematics, Higashi-Osaka, 577-8502 (Japan), Kyoto University, Institute for Mathematical Sciences, Kyoto, 606-8502 (Japan), Kyoto University, Department of Mathematics, Graduate School of Science, Kyoto, 606-8502 (Japan), Kyoto University, Research Institute for Mathematical Sciences, Kyoto, 606-8502 (Japan)

Annales de l’institut Fourier (2004)

- Volume: 54, Issue: 5, page 1393-1421
- ISSN: 0373-0956

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topAoki, Takashi, et al. "On the exact WKB analysis of microdifferential operators of WKB type." Annales de l’institut Fourier 54.5 (2004): 1393-1421. <http://eudml.org/doc/116146>.

@article{Aoki2004,

abstract = {We first introduce the notion of microdifferential operators of WKB type and then develop
their exact WKB analysis using microlocal analysis; a recursive way of constructing a WKB
solution for such an operator is given through the symbol calculus of microdifferential
operators, and their local structure near their turning points is discussed by a
Weierstrass-type division theorem for such operators. A detailed study of the Berk-Book
equation is given in Appendix.},

affiliation = {Kinki University, School of Science and Engineering, Department of Mathematics, Higashi-Osaka, 577-8502 (Japan), Kyoto University, Institute for Mathematical Sciences, Kyoto, 606-8502 (Japan), Kyoto University, Department of Mathematics, Graduate School of Science, Kyoto, 606-8502 (Japan), Kyoto University, Research Institute for Mathematical Sciences, Kyoto, 606-8502 (Japan)},

author = {Aoki, Takashi, Kawai, Takahiro, Koike, Tatsuya, Takei, Yoshitsugu},

journal = {Annales de l’institut Fourier},

keywords = {exact WKB analysis; microdifferential operators of WKB type; turning points; Weierstrass-type division theorem for microdifferential operators; Berk-Book equation},

language = {eng},

number = {5},

pages = {1393-1421},

publisher = {Association des Annales de l'Institut Fourier},

title = {On the exact WKB analysis of microdifferential operators of WKB type},

url = {http://eudml.org/doc/116146},

volume = {54},

year = {2004},

}

TY - JOUR

AU - Aoki, Takashi

AU - Kawai, Takahiro

AU - Koike, Tatsuya

AU - Takei, Yoshitsugu

TI - On the exact WKB analysis of microdifferential operators of WKB type

JO - Annales de l’institut Fourier

PY - 2004

PB - Association des Annales de l'Institut Fourier

VL - 54

IS - 5

SP - 1393

EP - 1421

AB - We first introduce the notion of microdifferential operators of WKB type and then develop
their exact WKB analysis using microlocal analysis; a recursive way of constructing a WKB
solution for such an operator is given through the symbol calculus of microdifferential
operators, and their local structure near their turning points is discussed by a
Weierstrass-type division theorem for such operators. A detailed study of the Berk-Book
equation is given in Appendix.

LA - eng

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

UR - http://eudml.org/doc/116146

ER -

## References

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