Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(10): 100303    DOI: 10.1088/1674-1056/19/10/100303
GENERAL Prev   Next  

Two new integrable couplings of the soliton hierarchies with self-consistent sources

Xia Tie-Cheng(夏铁成)
Department of Mathematics, Shanghai University, Shanghai 200444, China
Abstract  A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with $\widetilde{sl}$(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra $\widetilde{sl}$(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.
Keywords:  TC hierarchy      generalized Burgers hierarchy      self-consistent sources      integrable couplings      loop algebra  
Received:  26 October 2009      Revised:  29 March 2010      Accepted manuscript online: 
PACS:  02.10.Ud (Linear algebra)  
  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
Fund: Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800), the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806), the Shanghai Leading Academic Discipline Project (Grant No. J50101), the Key Disciplines of Shanghai Municipality (Grant No. S30104), and the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159).

Cite this article: 

Xia Tie-Cheng(夏铁成) Two new integrable couplings of the soliton hierarchies with self-consistent sources 2010 Chin. Phys. B 19 100303

[1] Kaup D J 1987 Phys. Rev. Lett. 59 2063
[2] Nakazawa M, Yomada E and Kubata H 1991 Phys. Rev. Lett. 66 2625
[3] Ma W X 2003 J. Phys. Soc. Jpn. 72 3017
[4] Ma W X 2005 Chaos, Solitions and Fractals 26 1453
[5] Zeng Y B, Ma W X and Lin R L 2000 wxJ. Math. Phys.41 5453
[6] Zeng Y B and Li Y S 1996 Acta Math. Appl. 12 337
[7] Deng S F 2008 Chin. Phys. Lett. 25 2331
[8] Deng S F 2008 Phys. Lett. A 372 460
[9] Yu F J and Li L 2009 Appl. Math. Comput. 207 171
[10] Yu F J 2008 Phys. Lett. A 372 6613
[11] Zhang Y F and Guo F K 2006 Commun. Theor. Phys. (Beijing, China) bf46 812
[12] Tu G Z 1989 J. Math. Phys. 30 330
[13] Xia T C, You F C and Chen D Y 2005 Chaos, Solitons and Fractals23 1911
[14] Xia T C and You F C 2006 Chaos, Solitons and Fractals28 938
[15] Dong H H and Wang X Z 2010 Chin. Phys. B 19 010202
[16] Dong H H and Yang H W 2009 Chin. Phys. B 18 845
[17] Guo F K and Zhang Y F 2005 J. Phys. A: Math. Gen.38 8537
[18] Ma W X 1992 Chin. J. Cont. Math.13 115
[19] Ma W X and Chen M 2006 J. Phys. A: Math. Gen.39 10787
[20] Tu G Z 1990 Northeastern Math. J. 6 26
[21] Yan Z Y 2003 J. Math. Phys.43 4978
[22] You F C and Xia T C 2008 Chaos, Solitons and Fractals 36 953
[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] Two new discrete integrable systems
Chen Xiao-Hong (陈晓红), Zhang Hong-Qing (张鸿庆). Chin. Phys. B, 2013, 22(3): 030203.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] 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.
[8] 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.
[9] The extended trace identity and its application
Yao Yu-Qin(姚玉芹) and Chen Deng-Yuan(陈登远). Chin. Phys. B, 2007, 16(3): 611-620.
[10] The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system
Xia Tie-Cheng (夏铁成), Wang Hong (汪宏), Zhang Yu-Feng (张玉峰). Chin. Phys. B, 2005, 14(2): 247-250.
[11] A type of multi-component integrable hierarchy
Zhang Yu-Feng (张玉峰), Zhang Yu-Sen (张玉森). Chin. Phys. B, 2004, 13(8): 1183-1186.
[12] A generalized SHGI integrable hierarchy and its expanding integrable model
Zhang Yu-Feng (张玉峰). Chin. Phys. B, 2004, 13(3): 307-311.
[13] A subalgebra of loop algebra $\tilde{A}_2$ and its applications
Zhang Yu-Feng (张玉峰), Tam Hon-Wah (谭汉华), Guo Fu-Kui (郭福奎). Chin. Phys. B, 2004, 13(2): 132-138.
[14] Two expanding forms of a Lie algebra and their application
Yan Qing-You (闫庆友), Zhang Yu-Feng (张玉峰), Wei Xiao-Peng (魏小鹏). Chin. Phys. B, 2003, 12(6): 581-585.
[15] An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system
Zhang Yu-Feng (张玉峰). Chin. Phys. B, 2003, 12(11): 1194-1201.
No Suggested Reading articles found!