Integrability of reductions of the discrete Korteweg-de Vries and potential Korteweg-de Vries equations

被引：12

作者：

Hone, A. N. W. ^{[1
]}

van der Kamp, P. H. ^{[2
]}

Quispel, G. R. W. ^{[2
]}

Tran, D. T. ^{[3
]}

机构：

[1] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury, Kent, England

[2] La Trobe Univ, Dept Math & Stat, Melbourne, Vic, Australia

[3] Univ New S Wales, Sch Math & Stat, Sydney, NSW, Australia

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2013年 / 469卷 / 2154期

基金：

澳大利亚研究理事会;

关键词：

partial difference equations; integrable maps; Poisson brackets; DIFFERENCE-EQUATIONS; SOLITON-EQUATIONS; CLUSTER ALGEBRAS; MAPS; MAPPINGS; SEQUENCES; INTEGRALS; SYSTEMS;

D O I：

10.1098/rspa.2012.0747

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We study the integrability of mappings obtained as reductions of the discrete Korteweg-de Vries (KdV) equation and of two copies of the discrete potential KdV (pKdV) equation. We show that the mappings corresponding to the discrete KdV equation, which can be derived from the latter, are completely integrable in the Liouville-Arnold sense. The mappings associated with two copies of the pKdV equation are also shown to be integrable.

引用

页数：23

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