An approach for generating enlarging integrable systems

被引：12

作者：

Zhang, Yufeng ^{[1
]}

Fan, Engui

机构：

[1] Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China

[2] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

来源：

PHYSICS LETTERS A | 2007年 / 365卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Lie algebra; integrable system; Hamiltonian structure;

D O I：

10.1016/j.physleta.2006.11.103

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

By constructing a type of antisymmetric matrix Lie algebra, a way to generate enlarging integrable systems is presented. The such integrable hierarchies are not integrable couplings, specially, their corresponding Hamiltonian structure can be obtained by the trace identity. As an application example, the enlarging integrable system and the Hamiltonian structure of the AKNS hierarchy are given. Finally, the explicit relations expressed by the formulae among the solutions of the stationary zero curvature equations are obtained. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：89 / 96

页数：8

共 13 条

[1]

Chen Z.J., SOLID STATE COMMUN, V141, P359, DOI [10.1016/j.ssc.2006.11.033, DOI 10.1016/J.SSC.2006.11.033]

[2] The quadratic-form identity for constructing the Hamiltonian structure of integrable systems [J].

Guo, FK ;

Zhang, YF .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (40) :8537-8548

[3] A family of expanding integrable models of AKNS hierarchy of equations [J].

Guo, FK ;

Zhang, YF .

ACTA PHYSICA SINICA, 2002, 51 (05) :951-954

[4]

Ma W X, 2000, METH APPL ANAL, V7, P21

[5] Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras [J].

Ma, Wen-Xiu ;

Chen, Min .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (34) :10787-10801

[6] A coupled AKNS-Kaup-Newell soliton hierarchy [J].

Ma, WX ;

Zhou, RG .

JOURNAL OF MATHEMATICAL PHYSICS, 1999, 40 (09) :4419-4428

[7] Semi-direct sums of Lie algebras and continuous integrable couplings [J].

Ma, WX ;

Xu, XX ;

Zhang, YF .

PHYSICS LETTERS A, 2006, 351 (03) :125-130

[8] Integrable theory of the perturbation equations [J].

Ma, WX ;

Fuchssteiner, B .

CHAOS SOLITONS & FRACTALS, 1996, 7 (08) :1227-1250

[9] THE TRACE IDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN-STRUCTURE OF INTEGRABLE SYSTEMS [J].

TU, GZ .

JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (02) :330-338

[10] Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy [J].

Zhang, WF ;

Fan, EG .

PHYSICS LETTERS A, 2006, 348 (3-6) :180-186

← 1 2 →