超 Broer-Kaup-Kupershmidt 族的非线性可积耦合及其哈密尔顿结构

数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 686-695.

超 Broer-Kaup-Kupershmidt 族的非线性可积耦合及其哈密尔顿结构

魏含玉^1,2|夏铁成¹|岳超^1,3

1.上海大学数学系上海 200444|2.周口师范学院数学与信息科学系河南周口 466001|3.泰山医学院信息工程学院山东泰安 271016

收稿日期:2012-06-06 修回日期:2013-04-28 出版日期:2013-08-25 发布日期:2013-08-25
基金资助:
国家自然科学基金 (11271008, 61072147, 11071159)、上海市教委重点学科(J50101)、上海大学重点学科(A.13-0101-12-004)、山东省自然科学基金(ZR2012AM021)和山东省优秀中青年科学家科研奖励基金(BS2011DX038)资助

Nonlinear Integrable Couplings of Super Broer-Kaup-Kupershmidt Hierarchy and Its Hamiltonian Structures

WEI Han-Yu^1,2, JIA Tie-Cheng¹, YUE Chao^1,3

1.Department of Mathematics,Shanghai University, Shanghai 200444;
2.Department of Mathematics and Information Science, Zhoukou Normal University, Henan Zhoukou 466001;
3.College of Information Engineering, Taishan Medical University, Shandong Taian 271016

Received:2012-06-06 Revised:2013-04-28 Online:2013-08-25 Published:2013-08-25

摘要/Abstract

摘要：

基于一类新的Lie超代数, 给出了超Broer-Kaup-Kupershmidt 族的非线性可积耦合, 它能约化成经典的Broer-Kaup-Kupershmidt 族的非线性可积耦合. 利用相应Loop超代数上的超迹恒等式, 得到了超Broer-Kaup-Kupershmidt 族的非线性可积偶的超哈密尔顿结构. 这种方法还可以推广到其它的超孤子族.

关键词: Lie超代数, 超迹恒等式, 超Broer-Kaup-Kupershmidt 族, 非线性可积耦合

Abstract:

Base on a kind of new Lie superalgebras, we present the nonlinear integrable couplings of the super Broer-Kaup-Kupershmidt hierarchy, which can be reduces to nonlinear integrable couplings of the classical Broer-Kaup-Kupershmidt hierarchy. Super trace identity over the corresponding loop superalgebras is used to obtain the super Hamiltonian structures for the nonlinear integrable couplings of the super Broer-Kaup-Kupershmidt hierarchy. This method can be generalized to other super soliton hierarchy.

Key words: Lie superalgebras, Super trace identity, Super Broer-Kaup-Kupershmidt hierarchy, Nonlinear integrable couplings

中图分类号:

35Q51

魏含玉, 夏铁成, 岳超. 超 Broer-Kaup-Kupershmidt 族的非线性可积耦合及其哈密尔顿结构[J]. 数学物理学报, 2013, 33(4): 686-695.

WEI Han-Yu, JIA Tie-Cheng, YUE Chao. Nonlinear Integrable Couplings of Super Broer-Kaup-Kupershmidt Hierarchy and Its Hamiltonian Structures[J]. Acta mathematica scientia,Series A, 2013, 33(4): 686-695.

参考文献

[1] Zhang Y F, Zhang H Q, Yan Q Y. Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy. Physics Letters A, 2002, 299: 543--548

[2] Xia T C, Yu F J, Chen D Y. The multi-component classical-Boussinesq hierarchy of soliton equations and its multi-component integrable coupling system. Chaos, Solitons and Fractals, 2005, 23: 1163--1167

[3] Ma W X, Xu X X, Zhang Y F. Semi-direct sums of Lie algebras and continuous integrable couplings. Physics Letters A, 2006, 351: 125--130

[4] Yu F J, Xia T C, Zhang H Q. The multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions. Chaos, Solitons and Fractals, 2006, 27: 1036--1041

[5] Xia T C, You F C. Multi-component Dirac equation hierarchy and its multi-component integrable couplings system. Chinese Physics, 2007, 16: 605--610

[6] Xia T C. Integrable couplings of classical-Boussinesq hierarchy and its Hamiltonian structure. Commun Theor Phys, 2010, 53: 25--27

[7] Ma W X, Fushssteiner B. Integrable theory of the perturbation equations. Chaos, Soliton and Fractals, 1996, 7: 1227--1250

[8] Ma W X, Fushssteiner B. The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy. Physics Letters A, 1996, 213: 49--55

[9] Ma W X. Nonlinear continuous integrable Hamiltonian couplings. Applied Mathematics and Computation, 2011, 217: 7238--7244

[10] Ma W X, Zhu Z N. Constructing nonlinear discrete integrable Hamiltonian couplings. Computers and Mathematics with Applications, 2010, 60: 2601--2608

[11] Tao S X, Xia T C. Lie algebra and Lie super algebra for integrable couplings of C-KdV hierarchy. Chin Phys Lett, 2010, 27: 040202

[12] Tao S X, Xia T C. The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure. Chin Phys B, 2010, 19: 070202

[13] Tao S X, Xia T C. Two super-integrable hierarchies and their super-Hamiltonian structures. Commun Nonlinear Sci Numer Simulat, 2011, 16: 127--132

[14] 陶司兴, 夏铁成. 超Broer-Kaup-Kupershmidt族的双非线性化. 数学年刊, 2012, 33A: 217--228

[15] Li Z, Dong H H, Yang H W. A super-soliton hierarchy and its super-Hamiltonian structure. Int J Theor Phys, 2009, 48: 2172--2176

[16] 季杰, 虞静, 董亚娟. 超AKNS方程新的可积分解. 数学物理学报, 2012, 32A: 424--432

[17] You F C. Nonlinear super integrable Hamiltonian couplings. J Math Phys, 2011, 52: 123510

[18] Ma W X, He J S, Qin Z Y. A supertrace identity and its applications to superintegrable systems. J Math Phys, 2008, 49: 033511