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Chin. Phys. B, 2009, Vol. 18(3): 845-849    DOI: 10.1088/1674-1056/18/3/001
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Multi-component Harry--Dym hierarchy and its integrable couplings as well as their Hamiltonian structures

Yang Hong-Wei(杨红卫) and Dong Huan-He(董焕河)
College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
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.
Keywords:  Hamiltonian structure      H--D hierarchy      quadratic-form identity  
Received:  27 August 2007      Revised:  28 July 2008      Accepted manuscript online: 
PACS:  05.45.Yv (Solitons)  
  02.10.-v (Logic, set theory, and algebra)  
  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  

Cite this article: 

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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