超广义Burgers方程族的非线性可积耦合及其Bargmann对称约束

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 694-704.

超广义Burgers方程族的非线性可积耦合及其Bargmann对称约束

方芳*(),胡贝贝,张玲

^{滁州学院数学与金融学院安徽滁州 239000}

收稿日期:2019-03-19 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 方芳 E-mail:fangfang7679@163.com
基金资助:
国家自然科学基金(11601055);安徽省自然科学研究项目基金(KJ2015B02);安徽省教育厅自然科学研究项目基金(KJ2017B10)

Nonlinear Integrable Couplings and Bargmann Symmetry Constraint of Super Generalized-Burgers Hierarchy

Fang Fang*(),Beibei Hu,Ling Zhang

^{School of Mathematical and Finance, Chuzhou University, Anhui Chuzhou 239000}

Received:2019-03-19 Online:2020-06-26 Published:2020-07-15
Contact: Fang Fang E-mail:fangfang7679@163.com
Supported by:
the NSFC(11601055);the Natural Science Research Project of Anhui Province(KJ2015B02);the Natural Science Research Project of Anhui Provincial Education Department(KJ2017B10)

摘要/Abstract

摘要：

基于李超代数，构造了超广义Burgers方程族的非线性可积耦合，并且利用超级恒等式得到了它的超Hamilton结构.此外，该文计算出超广义Burgers方程族的非线性可积耦合的Bargmann对称约束.

关键词: 李超代数, 超广义Burgers方程族的非线性可积耦合, 超Hamilton结构, 可积耦合, Bargmann对称约束

Abstract:

With the help of the enlarging Lie super algebra, we construct nonlinear integrable couplings for coupled generalized-Burgers hierarchy in this paper. Then, we establish its super-Hamiltonian structures by utilizing super trace identity. Furthermore, we obtain the Bargmann Symmetry Constraint of super generalized-Burgers hierarchy.

Key words: Enlarging Lie super algebra, Super generalized-Burgers hierarchy, Integrable couplings, Super-Hamiltonian structures, Bargmann symmetry constraint

中图分类号:

O175.29

方芳,胡贝贝,张玲. 超广义Burgers方程族的非线性可积耦合及其Bargmann对称约束[J]. 数学物理学报, 2020, 40(3): 694-704.

Fang Fang,Beibei Hu,Ling Zhang. Nonlinear Integrable Couplings and Bargmann Symmetry Constraint of Super Generalized-Burgers Hierarchy[J]. Acta mathematica scientia,Series A, 2020, 40(3): 694-704.

参考文献 34

1	Gürses M , Oguz O . A super AKNS scheme. Phys Lett A, 1985, 108, 437- 440 doi: 10.1016/0375-9601(85)90033-7
2	Chowdhury A R , Roy S . On the Bäckland transformation and Hamiltonian properties of superevaluation equations. J Math Phys, 1986, 27, 2464- 2468 doi: 10.1063/1.527309
3	Kupershmidt B A . A super Korteweg-de Vries equation:An integrable system. Phys Lett A, 1984, 102, 213- 215 doi: 10.1016/0375-9601(84)90693-5
4	Ma W X , He J S , Qin Z Y . A supertrace identity and its applications to superintegrable systems. J Math Phys, 2008, 49, 033511 doi: 10.1063/1.2897036
5	Tao S X , Xia T C , Shi H . Super-KN hierarchy and its super-Hamiltonian structure. Commun Theor Phys, 2011, 55, 391- 395 doi: 10.1088/0253-6102/55/3/03
6	You F C , Zhang J , Zhao Y . Super-Hamiltonian structures and conservation laws of a new Six-Component Super-Ablowitz-Kaup-Newell-Segur hierarchy. Abstract and Applied Analysis, 2014, 2014, 1- 7
7	Yu J , Ma W X , Ha J W , Chen S T . An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation. Commun Nonlin Sci Numer Simulat, 2017, 43, 151- 157 doi: 10.1016/j.cnsns.2016.06.033
8	Han J W , Yu J . A generalized super AKNS hierarchy associated with Lie superalgebra sl(2\|1) and its super bi-Hamiltonian structure. Commun Nonlin Sci Numer Simulat, 2017, 44, 258- 265 doi: 10.1016/j.cnsns.2016.08.009
9	Zhang J , You F C , Zhao Y . A new super extension of Dirac hierarchy. Abstract and Applied Analysis, 2014, 2014, 93- 98
10	Ye Y J, Li Z H, Shen S F, Li C X. A generalized super integrable hierarchy of Dirac type. 2016, Arxiv ID: 1604.03728
11	Fuchssteiner B. Coupling of completely integrable systems: the perturbation bundle//Clarkson P A. Applications of Analytic and Geometric Methods to Nonlinear Differential Equations. Dordrecht: Kluwer, 2009: 125-138
12	Zhang Y F , Guo F K . Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy. Chaos, Solitons and Fractals, 2007, 34 (2): 490- 495
13	Zhang Y F , Tam H W . New integrable couplings and Hamiltonian structure of the KN hierarchy and the DLW hierarchy. Commun Nonlin Sci Numer Simulat, 2008, 13 (3): 524- 533 doi: 10.1016/j.cnsns.2006.06.003
14	Ma W X , Zhang Y . Component-trace identities for hamiltonian structures. Applicable Analysis, 2010, 89 (4): 457- 472 doi: 10.1080/00036810903277143
15	Tao S X , Xia T C . Lie algebra and Lie super algebra for integrable couplingof C-KdV hierarchy. Chin Phys Lett, 2010, 27 (4): 5- 8
16	Ma W X . Nonlinear continuous integrable hamiltonian couplings. Appl Math Comput, 2011, 217, 7238- 7244
17	Ma W X , Zhu Z N . Constructing nonlinear discrete integrable Hamiltonian couplings. Appl Math Comput, 2010, 60, 2601- 2608 doi: 10.1016/j.camwa.2010.08.076
18	Tao S X , Xia T C . Nonlinear super integrable couplings of super Broer-Kaup-Kupershmidt hierarchy and its super Hamiltonian structures. Adv Math Phys, 2013, 2013, 1- 8
19	You F C , Zhang J . Nonlinear superintegrable couplings for supercoupled KdV hierarchy with self-consistent sources. Rep Math Phys, 2015, 76, 131- 140 doi: 10.1016/S0034-4877(15)00032-4
20	Xing X Z , Wu J Z , Geng X G . Nonlinear super integrable couplings of super classical Boussinesq hierarchy. J Appl Math, 2014, 2014, 726- 732
21	Hu B B , Ma W X , Xia T C , Zhang L . Nonlinear integrable couplings of a generalized super Ablowitz-Kaup-Newell-Segur hierarchy and its super bi-Hamiltonian structures. Math Meth Appl Sci, 2018, 41, 1565- 1577 doi: 10.1002/mma.4686
22	Cao C W . A cubic system which generates Bargmann potential and N-gappotential. Chin Quart J Math, 1988, 3 (1): 90- 96
23	曹策问. AKN族的Lax组的非线性化. 中国科学, 1989, 7, 691- 698
	Cao C W . Binary nonlinearization of AKN hierarchy. Chin Sci, 1989, 7, 691- 698
24	Zeng Y B , Li Y S . The constraints of potentials and the finite-dimensional integrable systems. J Math Phys, 1989, 30 (8): 1679- 1689 doi: 10.1063/1.528253
25	Cao C W . Nolinearization of the Lax system for AKNS hierarchy. Sci China Ser A, 1990, 3315, 528- 536
26	Cao C W , Geng X G . Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy. J Phy A Math Gen, 1990, 23 (18): 4117- 4125 doi: 10.1088/0305-4470/23/18/017
27	Cao C W , Geng X G . A monconfocal generator of involutive systems and three associated soliton hierarchies. J Math Phys, 1991, 32 (9): 2323- 2328 doi: 10.1063/1.529156
28	Cao C W . A classical integrable system and the involutive representation of solutions of the KdV equation. Acta Math Sinica, 1991, 7 (3): 216- 223 doi: 10.1007/BF02582998
29	Xia T C . Integrable couplings of classical-Boussinesq hierarchy and its Hamiltonian structure. Commun Theor Phys, 2010, 53, 25- 27 doi: 10.1088/0253-6102/53/1/06
30	Hu X B . An approach to generate superextentions of integrable systems. Phys A:Math General, 1997, 30, 619- 632 doi: 10.1088/0305-4470/30/2/023
31	Yang H X , Du J , Xu X X , Cui J P . Hamiltonian and Super-Hamiltonian systems of a hierarchy of soliton equations. Appl Math Comput, 2010, 217, 1497- 1508
32	Ma W X , He J S , Qin Z Y . A supertrance identity and its applications to superintegrable systems. J Math Phys, 2008, 49, 033511 doi: 10.1063/1.2897036
33	Yu J , Han J W , He J S . Binary nonlinearization of the super AKNS system under an implicit symmetry constraint. Phys A:Math Theo, 2009, 42, 465201 doi: 10.1088/1751-8113/42/46/465201
34	Zeng Y B , Ma W X , Lin R L . Integration of the soliton hierarchy with self-consistent sources. J Math Phys, 2000, 41, 5453- 5489 doi: 10.1063/1.533420

[1]	魏含玉,夏铁成,胡贝贝,张燕. 一个新的可积广义超孤子族及其自相容源、守恒律[J]. 数学物理学报, 2020, 40(1): 187-199.
[2]	夏冬, 夏铁成, 李德生. 分数阶超Yang族及其超哈密顿结构[J]. 数学物理学报, 2015, 35(2): 373-380.
[3]	张玲, 祝红玲. 超Li系统的Bargmann对称约束和双非线性化[J]. 数学物理学报, 2014, 34(5): 1287-1295.
[4]	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.
[5]	于发军. 一个广义Toda 孤子族的非线性可积耦合系统[J]. 数学物理学报, 2012, 32(5): 974-981.
[6]	夏铁成, 张登朋, 特木尔朝鲁. 带有自相容源的屠族新可积耦合[J]. 数学物理学报, 2012, 32(5): 941-949.
[7]	陈良云;张永正;孟道骥. 关于限制李超代数的分解[J]. 数学物理学报, 2007, 27(4): 577-583.
[8]	高锁刚, 张新禄. 交换环上某些线性李超代数的理想[J]. 数学物理学报, 2002, 22(4): 441-446.
[9]	匡乐满, 曾高坚, 王发伯. 李超代数OSP(1,2)的两分量相干态表示[J]. 数学物理学报, 1995, 15(2): 204-208.
[10]	孙昌璞. 李超代数不可分解表示的Boson-Fermion实现[J]. 数学物理学报, 1991, 11(2): 121-129.