Please wait a minute...
Chin. Phys. B, 2009, Vol. 18(3): 850-855    DOI: 10.1088/1674-1056/18/3/002
GENERAL Prev   Next  

Discrete integrable system and its integrable coupling

Li Zhu(李柱)
College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China
Abstract  This paper derives new discrete integrable system based on discrete isospectral problem. It shows that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Finally, integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.
Keywords:  isospectral problem      Hamiltonian structure      integrable coupling      semi-direct sums  
Received:  05 June 2008      Revised:  05 August 2008      Accepted manuscript online: 
PACS:  05.45.Yv (Solitons)  
  02.30.Ik (Integrable systems)  
  02.10.Ud (Linear algebra)  

Cite this article: 

Li Zhu(李柱) Discrete integrable system and its integrable coupling 2009 Chin. Phys. B 18 850

[1] A new six-component super soliton hierarchy and its self-consistent sources and conservation laws
Han-yu Wei(魏含玉) and Tie-cheng Xia(夏铁成). Chin. Phys. B, 2016, 25(1): 010201.
[2] Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)
Wang Xin-Zeng (王新赠), Dong Huan-He (董焕河). Chin. Phys. B, 2015, 24(8): 080201.
[3] A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures
Zhai Yun-Yun (翟云云), Geng Xian-Guo (耿献国), He Guo-Liang (何国亮). Chin. Phys. B, 2014, 23(6): 060201.
[4] Two new discrete integrable systems
Chen Xiao-Hong (陈晓红), Zhang Hong-Qing (张鸿庆). Chin. Phys. B, 2013, 22(3): 030203.
[5] A new generalized fractional Dirac soliton hierarchy and its fractional Hamiltonian structure
Wei Han-Yu (魏含玉), Xia Tie-Cheng (夏铁成 ). Chin. Phys. B, 2012, 21(11): 110203.
[6] A nonlinear discrete integrable coupling system and its infinite conservation laws
Yu Fa-Jun (于发军 ). Chin. Phys. B, 2012, 21(11): 110202.
[7] Nonlinear integrable couplings of a nonlinear Schrödinger–modified Korteweg de Vries hierarchy with self-consistent sources
Yang Hong-Wei (杨红卫), Dong Huan-He (董焕河), Yin Bao-Shu (尹宝树). Chin. Phys. B, 2012, 21(10): 100204.
[8] Prolongation structure for nonlinear integrable couplings of a KdV soliton hierarchy
Yu Fa-Jun(于发军) . Chin. Phys. B, 2012, 21(1): 010201.
[9] The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure
Tao Si-Xing (陶司兴), Xia Tie-Cheng (夏铁成). Chin. Phys. B, 2010, 19(7): 070202.
[10] Two new integrable couplings of the soliton hierarchies with self-consistent sources
Xia Tie-Cheng(夏铁成). Chin. Phys. B, 2010, 19(10): 100303.
[11] A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations
Wang Xin-Zeng(王新赠) and Dong Huan-He(董焕河) . Chin. Phys. B, 2010, 19(1): 010202.
[12] A new multi-component integrable coupling system for AKNS equation hierarchy with sixteen-potential functions
Yu Fa-Jun(于发军) and Li Li(李丽). Chin. Phys. B, 2009, 18(9): 3651-3656.
[13] Multi-component Harry--Dym hierarchy and its integrable couplings as well as their Hamiltonian structures
Yang Hong-Wei(杨红卫) and Dong Huan-He(董焕河). Chin. Phys. B, 2009, 18(3): 845-849.
[14] The multicomponent (2+1)-dimensional Glachette--Johnson (GJ) equation hierarchy and its super-integrable coupling system
Yu Fa-Jun(于发军) and Zhang Hong-Qing(张鸿庆). Chin. Phys. B, 2008, 17(5): 1574-1580.
[15] Non-isospectral integrable couplings of Ablowitz--Kaup--Newell--Segur (AKNS) hierarchy with self-consistent sources
Yu Fa-Jun (于发军), Li Li (李 丽). Chin. Phys. B, 2008, 17(11): 3965-3973.
No Suggested Reading articles found!