摘要
Ｐａｉｎｌｅｖｅ方程是六类最重要的Ｍ阶代数常微分方程．虽然Ｐａｉｎｌｅｖｅ是从纯粹数学的考虑发现这些方程的，但如今它们与许多数学和物理问题密切相关，且许多解析的，代数的和几何的性质不断被发现．本文介绍Ｐａｉｎｌｅｖｅ方程解析理论的基本内容，包括解的亚纯性，有理解；Ｂａｃｋｌｕｎｄ变换和某些进一步的结果，如高阶第Ｍ类Ｐａｉｎｌｅｖｅ方程的新研究，值分布性质以及一些未解决的问题，其中包括作者的一些新结果。
Painleve Equations are six most important second order algebraic diffrential equations. Although these equations were found by P. Painleve in 1900 for purely mathematical reason, they have appeared in several mathematical physics problems, more and more algebraic, geometric and analytic properties were found. In this paper, we introduce basic facts of analytic theory of the painleve equations, include the meromorphy of the solutions, rational solutions, Backlund transformation and some further results, such as new researches for the higher order second Painleve equation, properties of value distribution of solutions and some open problem.
出处
《数学进展》
CSCD
北大核心
2000年第6期481-489,共9页
Advances in Mathematics（China）
