On the linearization of the first and second Painleve equations

被引：14

作者：

Joshi, N. ^{[1
]}

Kitaev, A. V. ^{[2
]}

Treharne, P. A. ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[2] VA Steklov Math Inst, St Petersburg 191023, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2009年 / 42卷 / 05期

关键词：

LAX PAIRS; DEFORMATIONS;

D O I：

10.1088/1751-8113/42/5/055208

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We found Fuchs-Garnier pairs in 3 x 3 matrices for the first and second Painleve equations which are linear in the spectral parameter. As an application of our pairs for the second Painleve equation we use the generalized Laplace transform to derive an invertible integral transformation relating two of its Fuchs-Garnier pairs in 2 x 2 matrices with different singularity structures, namely, the pair due to Jimbo and Miwa and that found by Harnad, Tracy andWidom. Together with the certain other transformations it allows us to relate all known 2 x 2 matrix Fuchs-Garnier pairs for the second Painleve equation to the original Garnier pair.

引用

页数：18

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