Multidimensional Baker-Akhiezer functions and Huygens' Principle

被引：65
作者：
Chalykh O.A. [1 ]
Feigin M.V. [1 ,2 ]
Veselov A.P. [3 ,4 ]
机构：
[1] Dept. of Mathematics and Mechanics, Moscow State University, Moscow
[2] Independent University of Moscow, Moscow, 121002
[3] Department of Mathematical Sciences, Loughborough University, Loughborough
[4] Landau Inst. for Theor. Physics, Moscow, 117940
来源：
Communications in Mathematical Physics | 1999年 / 206卷 / 3期
关键词：
Huygens; Fundamental Solution; Hyperbolic Equation; Algebraic System; Special Configuration;
D O I：
10.1007/PL00005521
中图分类号：
学科分类号：
摘要：
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.
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页码：533 / 566
页数：33
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