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
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
