Hypergeometric functions as infinite-soliton tau functions

被引:23
作者
Orlov, AY [1 ]
机构
[1] Russian Acad Sci, PP Shirshov Oceanol Inst, Moscow, Russia
基金
俄罗斯基础研究基金会;
关键词
solitons; rational solutions; tau function; hypergeometric function; duality;
D O I
10.1007/s11232-006-0018-4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
It is known that resonant multisoliton solutions depend oil higher times and a set of parameters (integrals of motion). We show that soliton tau functions of the Toda lattice (and of the multicomponent Toda lattice) are tau functions of a dual hierarchy; where the higher times and the parameters (integrals of motion) exchange roles. The multisoliton solutions turn out to be rational solutions of the dual hierarchy, and the infinite-soliton tau functions turn out to be hypergeometric-type tau functions of the dual hierarchy. The variables in the dual hierarchies exchange roles. Soliton momenta are related to the Frobenius coordinates of partitions in the decomposition of rational solutions with respect to Schur functions. As an example, we consider partition functions of matrix models: their perturbation series is, oil one hand, a hypergeometric tau function and, on the other hand, can be interpreted as an infinite-soliton solution.
引用
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页码:183 / 206
页数:24
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