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.
Received: 03 June 2006
Revised: 12 September 2006
Accepted manuscript online:
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.