Discrete analogues of the Liouville equation

被引：78

作者：

Adler, VE ^{[1
]}

Startsev, SY

机构：

[1] Russian Acad Sci, Ufa Sci Ctr, Inst Math, Ufa 450001, Russia

[2] Russian Acad Sci, Ufa Sci Ctr, Ctr Computat, Ufa 450001, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 1999年 / 121卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.1007/BF02557219

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The notion of Laplace invariants is generalized to lattices and discrete equations that are difference analogues of hyperbolic partial differential equations with two independent variables. The sequence of Laplace invariants satisfies the discrete analogue of the two-dimensional Toda lattice. We prove that terminating this sequence by zeros is a necessary condition for the existence of integrals of the equation under consideration. We present formulas for the higher symmetries of equations possessing such integrals. We give examples of difference analogues of the Liouville equation.

引用

页码：1484 / 1495

页数：12

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