2013/12/06 by Kohei Iwaki, Iwaki, Kohei
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math.CA
paper · pdf · doi:10.48550/arxiv.1312.1874
55 pages, many figures. Version2: to appear in Publications of the Research Institute for Mathematical Sciences
openalex publication_date 2013/12/06 · arxiv created 2014/10/24 · arxiv updated 2014/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.