中国物理B ›› 2006, Vol. 15 ›› Issue (7): 1407-1413.doi: 10.1088/1009-1963/15/7/003

• GENERAL • 上一篇    下一篇

On the linearization of the coupled Harry－Dym soliton hierarchy

陈金兵, 耿献国   

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
  • 收稿日期:2005-10-28 修回日期:2006-04-13 出版日期:2006-07-20 发布日期:2006-07-20

On the linearization of the coupled Harry－Dym soliton hierarchy

Chen Jin-Bing (陈金兵), Geng Xian-Guo (耿献国)   

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
  • Received:2005-10-28 Revised:2006-04-13 Online:2006-07-20 Published:2006-07-20

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摘要： This paper is devoted to the study of the underlying linearities of the coupled Harry--Dym (cHD) soliton hierarchy, including the well-known cHD equation. Resorting to the nonlinearization of Lax pairs, a family of finite-dimensional Hamiltonian systems associated with soliton equations are presented, constituting the decomposition of the cHD soliton hierarchy. After suitably introducing the Abel--Jacobi coordinates on a Riemann surface, the cHD soliton hierarchy can be ultimately reduced to linear superpositions, expressed by the Abel--Jacobi variables.

Abstract: This paper is devoted to the study of the underlying linearities of the coupled Harry--Dym (cHD) soliton hierarchy, including the well-known cHD equation. Resorting to the nonlinearization of Lax pairs, a family of finite-dimensional Hamiltonian systems associated with soliton equations are presented, constituting the decomposition of the cHD soliton hierarchy. After suitably introducing the Abel--Jacobi coordinates on a Riemann surface, the cHD soliton hierarchy can be ultimately reduced to linear superpositions, expressed by the Abel--Jacobi variables.

Key words: soliton hierarchy, Hamiltonian systems, Riemann surface, Abel--Jacobi coordinates

中图分类号:  (Solitons)

  • 05.45.Yv
45.05.+x (General theory of classical mechanics of discrete systems)