Multiple-scale analysis for Painlevé transcendents with a large parameter

Takashi Aoki

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 11-17
  • ISSN: 0137-6934

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Aoki, Takashi. "Multiple-scale analysis for Painlevé transcendents with a large parameter." Banach Center Publications 39.1 (1997): 11-17. <http://eudml.org/doc/208654>.

@article{Aoki1997,
author = {Aoki, Takashi},
journal = {Banach Center Publications},
keywords = {WKB methods; reduction of equations; hypergeometric functions; Painlevé transcendents},
language = {eng},
number = {1},
pages = {11-17},
title = {Multiple-scale analysis for Painlevé transcendents with a large parameter},
url = {http://eudml.org/doc/208654},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Aoki, Takashi
TI - Multiple-scale analysis for Painlevé transcendents with a large parameter
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 11
EP - 17
LA - eng
KW - WKB methods; reduction of equations; hypergeometric functions; Painlevé transcendents
UR - http://eudml.org/doc/208654
ER -

References

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  1. [AKT1] T. Aoki, T. Kawai and Y. Takei, The Bender-Wu analysis and the Voros theory, in: ICM-90 Satellite Conf. Proc. ``Special Functions'' (M. Kashiwara and T. Miwa, editors), Springer-Verlag, 1991, 1-29. 
  2. [AKT2] T. Aoki, T. Kawai and Y. Takei, Algebraic analysis of singular perturbations - On exact WKB analysis, Sugaku Expositions 8 (1995), 217-240. 
  3. [AKT3] T. Aoki, T. Kawai and Y. Takei, WKB analysis of Painlevé transcendents with a large parameter, II, in preparation. Zbl0894.34050
  4. [BO] C. M. Bender and S. T. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978. Zbl0417.34001
  5. [JK] N. Joshi and M. Kruskal, Connection results for the first Painlevé equation, in: Painlevé transcendents (D. Levi and P. Winternitz, editors), Plenum Press, New York, 1992, 61-79. Zbl0856.34014
  6. [KT] T. Kawai and Y. Takei, WKB analysis of Painlevé transcendents with a large parameter, I, Adv. Math. 118 (1996), 1-33. Zbl0848.34005
  7. [V] A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. Inst. H. Poincaré Sect. A (N.S.) 39 (1983), 211-338. Zbl0526.34046

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