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.
Citation
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
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