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.
展开▼