Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(3): 030203    DOI: 10.1088/1674-1056/22/3/030203
GENERAL Prev   Next  

Two new discrete integrable systems

Chen Xiao-Hong (陈晓红)a b, Zhang Hong-Qing (张鸿庆)a
a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
b School of Science, University of Science and Technology Liaoning, Anshan 114051, China
Abstract  In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Â1. By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.
Keywords:  discrete integrable system      Hamiltonian structure      loop algebra  
Received:  11 May 2012      Revised:  01 November 2012      Accepted manuscript online: 
PACS:  02.30.Ik (Integrable systems)  
  03.40.Kf  
Corresponding Authors:  Chen Xiao-Hong     E-mail:  xhchspring@163.com

Cite this article: 

Chen Xiao-Hong (陈晓红), Zhang Hong-Qing (张鸿庆) Two new discrete integrable systems 2013 Chin. Phys. B 22 030203

[1] Wadati M 1976 Prog. Theor. Phys. Suppl. 59 36
[2] Ablowitz M J and Ladik J F 1975 J. Math. Phys. 16 598
[3] Kaup D J 2005 Math. Comput. Simulat. 69 322
[4] Toda M 1970 Theor. Phys. Suppl. 45 174
[5] Tu G Z 1900 J. Phys. A: Math. Gen. 23 3903
[6] Zhang D J and Chen D Y 2002 Chaos Soliton. Fract. 14 573
[7] Pickering A and Zhu Z N 2006 Phys. Lett. A 349 439
[8] Zhao Q L, Xu X X and Li X Y 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 1664
[9] Date E, Jinbo M and Miwa T 1982 J. Phys. Soc. Jpn. 51 4116
[10] Xu X X 2008 Phys. Lett. A 372 3683
[11] Zhu Z N 2007 J. Phys. A 40 7707
[12] Zhang Y F, Fan E G and Zhang Y Q 2006 Phys. Lett. A 357 454
[13] Yu F J and Zhang H Q 2006 Chaos Soliton. Fract. 29 1173
[14] Ma W X and Zhu Z N 2010 Compt. Math. Appl. 60 2601
[15] Guo F K and Zhang Y F 2002 Acta Phys. Sin. 51 951 (in Chinese)
[16] Wen X Y 2012 Appl. Math. Comp. 218 5796
[17] Taogetusang and Sirendaoerji 2009 Acta Phys. Sin. 58 5887 (in Chinese)
[18] Sirendaoerji and Taogetusang 2009 Acta Phys. Sin. 58 5894 (in Chinese)
[19] Zhang Y F 2004 Chin. Phys. 13 307
[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] Lattice soliton equation hierarchy and associated properties
Zheng Xin-Qing (郑新卿), Liu Jin-Yuan (刘金元). Chin. Phys. B, 2012, 21(9): 090202.
[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] 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.
[7] 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.
[8] 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.
[9] 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.
[10] Discrete integrable system and its integrable coupling
Li Zhu(李柱). Chin. Phys. B, 2009, 18(3): 850-855.
[11] An integrable Hamiltonian hierarchy and associated integrable couplings system
Chen Xiao-Hong(陈晓红), Xia Tie-Cheng(夏铁成), and Zhu Lian-Cheng(朱连成). Chin. Phys. B, 2007, 16(9): 2493-2497.
[12] Discrete integrable couplings associated with modified Korteweg--de Vries lattice and two hierarchies of discrete soliton equations
Dong Huan-He(董焕河). Chin. Phys. B, 2007, 16(5): 1177-1181.
[13] Two types of loop algebras and their expanding Lax integrable models
Yue Chao(岳超), Zhang Yu-Feng(张玉峰), and Wei Yuan(魏媛). Chin. Phys. B, 2007, 16(3): 588-594.
[14] The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure
Yue Chao(岳超), Yang Geng-Wen(杨耕文), and Xu Yue-Cai(许曰才). Chin. Phys. B, 2007, 16(3): 595-598.
[15] Multi-component Dirac equation hierarchy and its multi-component integrable couplings system
Xia Tie-Cheng(夏铁成) and You Fu-Cai(尤福财). Chin. Phys. B, 2007, 16(3): 605-610.
No Suggested Reading articles found!