Constructing nonlinear discrete integrable Hamiltonian couplings

被引：69

作者：

Ma, Wen-Xiu ^{[1
]}

Zhu, Zuo-Nong ^{[2
]}

机构：

[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 60卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Integrable couplings; Hamiltonian structures; Variational identities; LIE-ALGEBRAS; SOLITON-EQUATIONS; SEMIDIRECT SUMS; BACKLUND-TRANSFORMATIONS; PERTURBATION EQUATIONS; SPECTRAL PROBLEM; HIERARCHY; SYSTEMS; IDENTITIES;

D O I：

10.1016/j.camwa.2010.08.076

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing nonlinear discrete integrable couplings. Discrete variational identities over the associated loop algebras are used to build Hamiltonian structures for the resulting integrable couplings. We illustrate the application of the scheme by means of an enlarged Volterra spectral problem and present an example of nonlinear discrete integrable Hamiltonian couplings for the Volterra lattice equations. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2601 / 2608

页数：8

共 32 条

[1] New integrable hierarchies from vertex operator representations of polynomial Lie algebras
Casati, P
Ortenzi, G
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2006, 56 (03) : 418 - 449
[2] A hierarchy of nonlinear lattice soliton equations, its integrable coupling systems and infinitely many conservation laws
Ding, Hai-Yong
Sun, Ye-Peng
Xu, Xi-Xiang
[J]. CHAOS SOLITONS & FRACTALS, 2006, 30 (01) : 227 - 234
[3] A unified expressing model of the AKNS hierarchy and the KN hierarchy, as well as its integrable coupling system
Guo, FK
Zhang, YF
[J]. CHAOS SOLITONS & FRACTALS, 2004, 19 (05) : 1207 - 1216
[4] Two integrable couplings of the Tu hierarchy and their Hamiltonian structures
Li, Zhu
Dong, Huanhe
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 55 (11) : 2643 - 2652
[5] NEW INTEGRABLE LATTICE HIERARCHY AND ITS INTEGRABLE COUPLING
Li, Zhu
Dong, Huanhe
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2009, 23 (23): : 4791 - 4800
[6] Ma W.X., 2000, METHODS APPL ANAL, V7, P21
[7] COUPLING INTEGRABLE COUPLINGS
Ma, Wen Xiu
Gao, Liang
[J]. MODERN PHYSICS LETTERS B, 2009, 23 (15): : 1847 - 1860
[8] A discrete variational identity on semi-direct sums of Lie algebras
Ma, Wen-Xiu
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (50) : 15055 - 15069
[9] A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order
Ma, Wen-Xiu
[J]. PHYSICS LETTERS A, 2007, 367 (06) : 473 - 477
[10] Semidirect sums of Lie algebras and discrete integrable couplings
Ma, Wen-Xiu
Xu, Xi-Xiang
Zhang, Yufeng
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (05)

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