中国物理B ›› 2007, Vol. 16 ›› Issue (2): 296-302.doi: 10.1088/1009-1963/16/2/005

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A new high-order spectral problem of the mKdV and its associated integrable decomposition

季杰1, 姚玉芹1, 刘玉清2, 虞静3   

  1. (1)Department of Mathematics, Shanghai University, Shanghai 200444, China; (2)Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Information Science, Jiangsu Polytechnic University, Changzhou 213016, China; (3)Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2006-04-17 修回日期:2006-08-28 出版日期:2007-02-20 发布日期:2007-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10371070), the Special Funds for Major Specialities of Shanghai Educational Committee.

A new high-order spectral problem of the mKdV and its associated integrable decomposition

Ji Jie(季杰)a)†, Yao Yu-Qin(姚玉芹)a), Yu Jing(虞静)b), and Liu Yu-Qing(刘玉清)a)c)   

  1. a Department of Mathematics, Shanghai University, Shanghai 200444, China; b Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; c Department of Information Science, Jiangsu Polytechnic University, Changzhou 213016, China
  • Received:2006-04-17 Revised:2006-08-28 Online:2007-02-20 Published:2007-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10371070), the Special Funds for Major Specialities of Shanghai Educational Committee.

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摘要： A new approach to formulizing a new high-order matrix spectral problem from a normal 2× 2 matrix modified Korteweg--de Vries (mKdV) spectral problem is presented. It is found that the isospectral evolution equation hierarchy of this new higher-order matrix spectral problem turns out to be the well-known mKdV equation hierarchy. By using the binary nonlinearization method, a new integrable decomposition of the mKdV equation is obtained in the sense of Liouville. The proof of the integrability shows that r-matrix structure is very interesting.

关键词: spectral problem, integrable decomposition, mKdV equation hierarchy

Abstract: A new approach to formulizing a new high-order matrix spectral problem from a normal 2× 2 matrix modified Korteweg--de Vries (mKdV) spectral problem is presented. It is found that the isospectral evolution equation hierarchy of this new higher-order matrix spectral problem turns out to be the well-known mKdV equation hierarchy. By using the binary nonlinearization method, a new integrable decomposition of the mKdV equation is obtained in the sense of Liouville. The proof of the integrability shows that r-matrix structure is very interesting.

Key words: spectral problem, integrable decomposition, mKdV equation hierarchy

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.30.Ik (Integrable systems)