中国物理B ›› 2007, Vol. 16 ›› Issue (3): 611-620.doi: 10.1088/1009-1963/16/3/009

• GENERAL • 上一篇    下一篇

The extended trace identity and its application

姚玉芹, 陈登远   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • 收稿日期:2006-06-03 修回日期:2006-09-12 出版日期:2007-03-20 发布日期:2007-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10371070 and 10547123).

The extended trace identity and its application

Yao Yu-Qin(姚玉芹)† and Chen Deng-Yuan(陈登远)   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2006-06-03 Revised:2006-09-12 Online:2007-03-20 Published:2007-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10371070 and 10547123).

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摘要： The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable systems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell (M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy separately.

Abstract: The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable systems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell (M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy separately.

Key words: loop algebra, Killing form, trace identity, Hamiltonian structure

中图分类号:  (Solitons)

  • 05.45.Yv
02.10.Ud (Linear algebra) 02.30.Ik (Integrable systems)