中国物理B ›› 2009, Vol. 18 ›› Issue (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

杨红卫, 董焕河   

  1. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
  • 收稿日期:2007-08-27 修回日期:2008-07-28 出版日期:2009-03-20 发布日期:2009-03-20

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)   

  1. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
  • Received:2007-08-27 Revised:2008-07-28 Online:2009-03-20 Published:2009-03-20

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摘要： 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.

关键词: Hamiltonian structure, H--D hierarchy, quadratic-form identity

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.

Key words: Hamiltonian structure, H--D hierarchy, quadratic-form identity

中图分类号:  (Solitons)

  • 05.45.Yv
02.10.-v (Logic, set theory, and algebra) 02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)