Toda systems and hypergeometric equations

Autor:	Lin, Chang-Shou, Nie, Zhaohu, Wei, Juncheng
Rok vydání:	2016
Předmět:	Mathematics - Analysis of PDEs Mathematics - Algebraic Geometry Mathematics - Differential Geometry Nonlinear Sciences - Exactly Solvable and Integrable Systems 35J47 33C20
Druh dokumentu:	Working Paper
Popis:	This paper establishes certain existence and classification results for solutions to $SU(n)$ Toda systems with three singular sources at 0, 1, and $\infty$. First, we determine the necessary conditions for such an $SU(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions for $SU(n)$ Toda systems that satisfy the necessary conditions and also the interlacing conditions from Beukers and Heckman. Finally, for $SU(3)$ Toda systems satisfying the necessary conditions, we classify, under a natural reality assumption, that all the solutions are related to hypergeometric equations. This proof uses the Pohozaev identity. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1610.03194 Zobrazit plný text záznamu View this record from Arxiv