Study of Solving a Toda Dynamic System with Loop Algebra

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

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

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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

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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

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

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