WKB analysis of higher order Painlevé equations with a large parameter—Local reduction of 0-parameter solutions for Painlevé hierarchies (PJ)(J=I,II-1 or II-2)

AbstractWe generalize the reduction theorem for 0-parameter solutions of a traditional (i.e., second order) Painlevé equation with a large parameter to those of some higher order Painlevé equation, that is, each member of the Painlevé hierarchies (PJ)(J=I,II-1 or II-2). Thus the scope of applicability of the reduction theorem in [KT1] has been substantially enlarged; only six equations were covered by our previous result, while Theorem 3.2.1 of this paper applies to infinitely many equations