Two super-integrable hierarchies and their super-Hamiltonian structures

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 1, 2011, Pages 127-132

  Tao, Sixing ^a,b   Xia, Tiecheng ^b  

^a SHANGQIU NORMAL UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Lie super algebra; Super Hamiltonian structure; Super integrable system; Super trace identity

Indexed keywords

HAMILTONIANS;

HAMILTONIAN STRUCTURES; INTEGRABLE HIERARCHY; INTEGRABLE SYSTEMS; ISOSPECTRAL PROBLEMS; LIE SUPER ALGEBRA; SUPER-HAMILTONIAN STRUCTURE; SUPER-INTEGRABLE SYSTEM; SUPER-TRACE IDENTITY; TRACE IDENTITIES; ZERO-CURVATURE EQUATION;

ALGEBRA;

EID: 77955926759     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.04.009     Document Type: Article

References (18)

1. Tu Guizhang The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. J Math Phys 1989, 30(2):330-338.
2. Tu Guizhang A trace identity and its application to the theory of discrete integrable systems. J Phys A Math Gen 1990, 23:3903-3922.
3. Ma Wenxiu A new hierarchy of Liouville integrable generalized Hamiltonian equations and its reduction. Chin J Contemp Math 1992, 13(1):79-89.
4. Ma Wenxiu, Fuchssteiner Benno Integrable theory of the perturbation equations. Chaos Solitons Fractals 1996, 7(8):1227-1250.
5. Guo Fukui, Zhang Yufeng The quadratic-form identity for constructing the Hamiltonian structure of integrable systems. J Phys A Math Gen 2005, 38:8537-8548.
6. Ma Wenxiu, Chen Min Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras. J Phys A Math Gen 2006, 39:10787-10801.
7. Ma Wenxiu, Zhou Zixiang Coupled integrable systems associated with a polynomial spectral problem and their Virasoro symmetry algebras. Prog Theoret Phys 1996, 96(2):449-457.
8. Zhang Yufeng A general Boite-Pempinelli-Tu hierarchy and its bi-Hamiltonian structure. Phys Lett A 2003, 317(3):280-286.
9. Fan Engui A Liouville integrable Hamiltonian system associated with a generalized Kaup-Newell spectral problem. Physica A 2001, 301:105-113.
10. Tu Guizhang On Liouville integrability of zero curvature equations and the Yang hierarchy. J Phys A Math Gen 1989, 22:2375-2392.
11. Xingbiao Hu. Integrable systems and related problems. Doctoral Dissertation. Computing Center of Chinese Academia Sinica; 1990.
12. Palit S., Roy Chowdhury A. Heisenberg subalgebra, dressing approach and super bi-Hamiltonian integrable system. J Phys A Math Gen 1994, 27:L311-L316.
13. Hu Xingbiao An approach to generate superextensions of integrable systems. J Phys A Math Gen 1997, 30:619-632.
14. Ma Wenxiu, He Jingsong, Qin Zhenyun A supertrace identity and its applications to superintegrable systems. J Math Phys 2008, 49:033511.
15. Dong Huanhe, Wang Xinzeng Lie algebra and Lie super algebra for the integrable couplings of NLS-MKdV hierarchy. Commun Nonlinear Sci Numer Simulat 2009, 14:4071-4077.
16. 2 and its associated two types of loop algebra, as well as Hamiltonian structures of integrable hierarchy. J Math Phys 2009, 50:053519.
17. Wang Xinzeng, Liu Xikui Two types of Lie super-algebra for the super-integrable Tu-hierarchy and its super- Hamiltonian structure. Commun Nonlinear Sci Numer Simulat 2005, 15:2044-2049.
18. Sun Hongzhou, Han Qizhi Lie algebras and Lie super algebras and their applications in physics 1999, Peking University Press, Beijing.