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)
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
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.
Received: 17 April 2006
Revised: 28 August 2006
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10371070), the Special
Funds for Major Specialities of Shanghai Educational
Committee.
Cite this article:
Ji Jie(季杰), Yao Yu-Qin(姚玉芹), Yu Jing(虞静), and Liu Yu-Qing(刘玉清) A new high-order spectral problem of the mKdV and its associated integrable decomposition 2007 Chinese Physics 16 296
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