Study of Solving a Toda Dynamic System with Loop Algebra

ZHU Qiao; YANG Zhan-Ying; SHI Kang-Jie; WEN Jun-Qing

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2006, Vol. 30> Issue(9) : 838-843

Study of Solving a Toda Dynamic System with Loop Algebra

Institute of Science, Shaanxi University of Science & Technology, Xianyang 712081, China2 Department of Physics, Northwest University, Xi'an 710069, China3 Institute of Modern Physics, Northwest University, Xi'an 710069, China4 Institute of Science, Xi'an Shiyou University, Xi'an 710065, China

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper, we construct a Toda system with Loop algebra, and prove that the Lax equation L=[L,M] can be solved by means of solving a regular Riemann-Hilbert problem. In our system, M in Lax pair is an antisymmetrical matrix, while L=L⁺+M, and L⁺ is a quasi-upper triangular matrix of loop algebra. In order to check our result, we exactly solve a R-H problem under a given initial condition as an example.

References

[1]

. Toda M J. Phys. Soc. Japan, 1967, 23: 501-5062. Castro-Alvaredo O A, Fring A. Applications of QuantumIntegrable Systems. arXiv:hep-th/03011023. JIANG Jin-Huan, LI Ai-Min, LI Zi-Ping. HEP NP, 2003,27(6): 489-492(in Chinese)(江金环，李爱民，李子平.高能物理与核物理，2003, 27(6):489-492)4. YANG Zhan-Ying, ZHEN Yi. HEP NP, 2000, 24(6):484-489(in Chinese)(杨战营，甄翼.高能物理与核物理，2000, 24(6): 484-489)5. YANG Zhan-Ying, ZHAO Liu, ZHEN Yi. HEP NP, 2000,24(4): 1-7(in Chinese)(杨战营，赵柳，甄翼.高能物理与核物理，2000, 24(4): 1-7)6. Nirov K S, Razumov A V. Higher Symmetries of TodaEquations. arXiv:hep-th/02101367. Toda M. Prog. Theor. Phys. Suppl., 1970, 45: 174-2008. Moser J. Adv. Math., 1975, 16: 197-220; Birkhauser.Basel, Prog. in Math., 1980, 8: 233-2899. Ruijsenaars S N M. Commun. Math. Phys., 1987, 110:191-21310. LIU Wang-Yun, YANG Zhan-Ying, ZHAO Liu. HEP NP,2004, 28(4): 359-364(in Chinese)(朱桥，杨战营，石康杰.高能物理与核物理，2005, 29(1): 19-22)11. ZHAO Liu, LIUWang-Yun. Commun. Theore. Phys., 2004,42: 9-1812. ZHU Qiao, YANG Zhan-Ying, SHI Kang-Jie. HEP NP,2005, 29(1): 19-2213. HUANG Lie-De. Advances in Mathematics, 1990, 19(2):265-283(in Chinese)(黄烈德.数学进展，1990, 19(2): 265-283)

[1]	SUN Yi , ZHANG Hao-Ran . One loop integrals reduction. Chinese Physics C, 2012, 36(11): 1055-1064. doi: 10.1088/1674-1137/36/11/004
[2]	SU Nan , Jens O , Michael Strickland . Hard-thermal-loop QED thermodynamics. Chinese Physics C, 2010, 34(9): 1527-1529. doi: 10.1088/1674-1137/34/9/091
[3]	JIANG Yun-Guo , HUANG Yong-Chang . Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System. Chinese Physics C, 2006, 30(12): 1151-1155.
[4]	ZHU Qiao , YANG Zhan-Ying , SHI Kang-Ji . The Study on Generalized Toda Mechanics System with Loop Algebra L(D^r). Chinese Physics C, 2005, 29(1): 19-22.
[5]	ZHAO Xiao-Yan , ZHENG Jian-Hua , WANG Yi-Fang , ZHAO Zhi-Zheng , ZU Kai-Ling . A New Detecting System of the Beam Profile. Chinese Physics C, 2004, 28(11): 1184-1187.
[6]	LIU Wang-Yun , YANG Zhan-Ying , ZHAO Liu . Generalized Toda Mechanics Associated with Classical Lie Algebras D_r. Chinese Physics C, 2004, 28(4): 359-364.
[7]	LIU Bo , GUO Hua . Equation of State for the Thermal System of Nuclear Matter. Chinese Physics C, 2003, 27(7): 590-593.
[8]	HUANG Sheng-Li , XU Zi-Zong , WANG Zhao-Min , WANG Xiao-Lian , LI Cheng , CHEN Hong-Fang , WU Jian , ZENG Hui . A Precise Trigger Timing System. Chinese Physics C, 2002, 26(9): 959-963.
[9]	YANG ZhanYing , ZHEN Yi . Construction on the Solution of osp(1｜4)Toda Model. Chinese Physics C, 2000, 24(6): 484-489.
[10]	Li Fengtian , Xie Jialin , Wang Yanshan , Wang Bosi . A Novel Control System for RF Power System of LINAC. Chinese Physics C, 1998, 22(10): 932-936.
[11]	ZHAO Liu . From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories. Chinese Physics C, 1993, 17(5): 431-443.
[12]	ZHAO Liu , YANG Wen-Li . Bosonic Superconformal Toda Model and Dressing Transformation. Chinese Physics C, 1993, 17(4): 338-344.
[13]	Zhao Liu , Yang Wenli . Bosonic Superconformal Toda Theory and Dressing Symmetry. Chinese Physics C, 1993, 17(S1): 65-72.
[14]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅰ) General Framework. Chinese Physics C, 1993, 17(1): 28-37.
[15]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅱ)An Example. Chinese Physics C, 1993, 17(3): 241-251.
[16]	HOU Bo-Yu , ZHAO Liu , YANG Huan-Xiong . Affine Toda Fields as Restriced WZNW Model. Chinese Physics C, 1991, 15(8): 701-710.
[17]	XU Jian-Ming , XU Qing . ANALYSIS OF THE PERFORMANCE OF A NEW TYPE OF LINEAR PERIODIC MAGNETS. Chinese Physics C, 1988, 12(4): 513-520.
[18]	ZHONG Ji-Quan , GE Ling-Xiao , LIU Jian-Ye , YU Xian . A DYNAMICAL METHOD IN DEEP IN ELASTIC COLLISION OF HEAVY IONS. Chinese Physics C, 1983, 7(5): 598-604.
[19]	ZHU Wei , SHEN Jian-Guo . A DYNAMICAL MODEL FOR THE GLUON DISTRIBUTION FUNCTION. Chinese Physics C, 1983, 7(3): 316-322.
[20]	Wei Kai-yu , Lin Zhen-hua . A COMPUTATIONAL METHOD FOR THE DESIGN ENERGY HIGH INTENSITY BEAM TRANSPORT SYSTEMS. Chinese Physics C, 1980, 4(5): 555-562.

Access

Get Citation

ZHU Qiao, YANG Zhan-Ying, SHI Kang-Jie and WEN Jun-Qing. Study of Solving a Toda Dynamic System with Loop Algebra[J]. Chinese Physics C, 2006, 30(9): 838-843.

ZHU Qiao, YANG Zhan-Ying, SHI Kang-Jie and WEN Jun-Qing. Study of Solving a Toda Dynamic System with Loop Algebra[J]. Chinese Physics C, 2006, 30(9): 838-843. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2005-12-17
Revised: 2006-04-22

Article Metric

Article Views(3225)
PDF Downloads(511)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, [email protected]

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Study of Solving a Toda Dynamic System with Loop Algebra

Corresponding author: ZHU Qiao,

Institute of Science, Shaanxi University of Science & Technology, Xianyang 712081, China2 Department of Physics, Northwest University, Xi'an 710069, China3 Institute of Modern Physics, Northwest University, Xi'an 710069, China4 Institute of Science, Xi'an Shiyou University, Xi'an 710065, China

Received Date: 2005-12-17
Accepted Date: 2006-04-22
Available Online: 2006-09-05

Abstract: In this paper, we construct a Toda system with Loop algebra, and prove that the Lax equation L=[L,M] can be solved by means of solving a regular Riemann-Hilbert problem. In our system, M in Lax pair is an antisymmetrical matrix, while L=L⁺+M, and L⁺ is a quasi-upper triangular matrix of loop algebra. In order to check our result, we exactly solve a R-H problem under a given initial condition as an example.