On WKB theoretic transformations for Painleve transcendents on degenerate Stokes segments
Abstract
The WKB theoretic transformation theorem established in [KT2] implies that the first Painleve equation gives a normal form of Painleve equations with a large parameter near a simple P-turning point. In this paper we extend this result and show that the second Painleve equation (PII) and the third Painleve equation (PIII'(D7)) of type D7 give a normal form of Painleve equations on a degenerate P-Stokes segments connecting two different simple P-turning points and on a degenerate P-Stokes segment of loop-type, respectively. That is, any 2-parameter formal solution of a Painleve equation is reduced to a 2-parameter formal solution of (PII) or (PIII'(D7)) on these degenerate P-Stokes segments by our transformation.
Keywords
Cite
@article{arxiv.1312.1874,
title = {On WKB theoretic transformations for Painleve transcendents on degenerate Stokes segments},
author = {Kohei Iwaki},
journal= {arXiv preprint arXiv:1312.1874},
year = {2014}
}
Comments
55 pages, many figures. Version2: to appear in Publications of the Research Institute for Mathematical Sciences