Multidimensional Baker–Akhiezer Functions and Huygens' Principle
Multidimensional Baker–Akhiezer Functions and Huygens' Principle
复制标题
多维 Baker–Akhiezer 函数和惠更斯原理
DOI：
10.1007/pl00005521
复制
发表时间：
1999
影响因子：
2.4
通讯作者：
A. Veselov
中科院分区：
文献类型：
--
作者：
O. Chalykh;Misha Feigin;A. Veselov
翻译后摘要：合理的贝克-Akhiezer（BA）功能的概念，在Cn超平面的配置有关。证明了BA函数只存在于满足一定超定代数系统的特殊构形（轨迹构形）中。BA函数满足一些代数可积的薛定谔方程，因此任何轨迹配置都确定这样的方程。所有轨迹配置的分类的一些结果。这个理论被应用到著名的Hadamard问题描述的所有双曲型方程满足惠更斯原理。我们证明，在某一类中，所有此类方程都与轨迹配置有关，并且可以从BA函数显式构造相应的基本解。
Abstract:A notion of the rational Baker–Akhiezer (BA) function related to a configuration of hyperplanes in Cn is introduced. It is proved that the BA function exists only for very special configurations (locus configurations), which satisfy a certain overdetermined algebraic system. The BA functions satisfy some algebraically integrable Schrödinger equations, so any locus configuration determines such an equation. Some results towards the classification of all locus configurations are presented. This theory is applied to the famous Hadamard problem of description of all hyperbolic equations satisfying Huygens' Principle. We show that in a certain class all such equations are related to locus configurations and the corresponding fundamental solutions can be constructed explicitly from the BA functions.