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May 2004 On WKB analysis of higher order Painlevé equations with a large parameter
Takahiro Kawai, Yoshitsugu Takei
Proc. Japan Acad. Ser. A Math. Sci. 80(5): 53-56 (May 2004). DOI: 10.3792/pjaa.80.53

Abstract

We announce a generalization of the reduction theorem for 0-parameter solutions of the traditional (i.e., second order) Painlevé equations with a large parameter to those of some higher order Painlevé equations, i.e., each member of the Painlevé hierarchies $(P_J)$ ($J = \mbox{I}$, II-1 and II-2) discussed in [KKNT]. Thus the scope of applicability of the reduction theorem ([KT1, KT2]) has been substantially enlarged; only six equations were covered by our previous result, while the result reported here applies to infinitely many equations.

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Takahiro Kawai. Yoshitsugu Takei. "On WKB analysis of higher order Painlevé equations with a large parameter." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 53 - 56, May 2004. https://doi.org/10.3792/pjaa.80.53

Information

Published: May 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1067.34088
MathSciNet: MR2062800
Digital Object Identifier: 10.3792/pjaa.80.53

Subjects:
Primary: 34E20 , 34M55
Secondary: 33E17 , 34M40

Keywords: Lax pair , Painlevé hierarchy , Painlevé transcendent , turning point

Rights: Copyright © 2004 The Japan Academy

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Vol.80 • No. 5 • May 2004
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