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

作　　者：季杰 姚玉芹 虞静 刘玉清 

机构地区：[1]Department of Mathematics, Shanghai University, Shanghai 200444, China [2]Department of Mathematics, University of Science and Technology of China, Hefei 230026, China [3]Department of Information Science, Jiangsu Polytechnic University, Changzhou 213016, China

出　　处：《Chinese Physics B》2007年第2期296-302,共7页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China （Grant No 10371070）, the Special Funds for Major Specialities of Shanghai Educational Committee.Acknowledgments The authors express their appreciation to Professor Zhou Ru-Guang, Professor Qiao Zhi-Jun, Professor Chen Deng-Yuan and Professor Zhang Da-Jun for their valuable suggestions and help.

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,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 

分 类 号：O151.21[理学—数学]