The extended trace identity and its application |
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| Authors: | Yao Yu-Qin and Chen Deng-Yuan |
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| Affiliation: | Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | The trace identity is extended to the general loop algebra. TheHamiltonian structures of the integrable systems concerning vectorspectral problems and the multi-component integrable hierarchy can beworked out by using the extended trace identity. As itsapplication, we have obtained the Hamiltonian structures of the Yanghierarchy, the Korteweg-de--Vries (KdV) hierarchy, themulti-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, themulti-component Ablowitz--Kaup--Newell--Segur Kaup--Newell(M-AKNS--KN) hierarchy and a new multi-component integrable hierarchyseparately. |
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| Keywords: | loop algebra Killing form trace identity Hamiltonian structure |
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