Abstract This paper obtains the multi-component Harry--Dym (H--D) hierarchy and its integrable couplings by using two kinds of vector loop algebras $\widetilde{G}_3$ and $\widetilde{G}_6$. The Hamiltonian structures of the above system are given by the quadratic-form identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies.
Received: 27 August 2007
Revised: 28 July 2008
Accepted manuscript online:
Yang Hong-Wei(杨红卫) and Dong Huan-He(董焕河) Multi-component Harry--Dym hierarchy and its integrable couplings as well as their Hamiltonian structures 2009 Chin. Phys. B 18 845
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