Loop Algebras and Bi-integrable Couplings  

作　　者：Wenxiu MA 

机构地区：[1]Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA.

出　　处：《Chinese Annals of Mathematics,Series B》2012年第2期207-224,共18页数学年刊（B辑英文版）

基　　金：Project supported by the State Administration of Foreign Experts Affairs of China;the National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159);the Chunhui Plan of the Ministry of Education of China;the Innovation Project of Zhejiang Province (No.T200905);the Natural Science Foundation of Shanghai (No.09ZR1410800);the Shanghai Leading Academic Discipline Project (No.J50101)

摘　　要：A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.

关 键 词：Loop algebra Bi-integrable coupling Zero curvature equation SYMMETRY Hamiltonian structure 

分 类 号：O175.26[理学—数学] TK311[理学—基础数学]