摘要
Firstly 4 Lie algebras are constructed. Then applications of the loop algebra are presented to obtain two types of coupling integrable couplings of the S-mKdV hierarchy by using Tu scheme. The coupling integrable couplings of the S-mKdV hierarchy obtained in the paper reduce to the coupling integrable couplings of the mKdV equation and the coupling integrable couplings of the nonlinear Schrodinger equation respectively. The method given in the paper can be used to other hierarchies generally.
基金
Supported by National Natural Science Foundation of China under Grant No. 10901090, the Natural Science Foundation of Shandong Province under Grant No. ZR2010AM029, and the Innovative Scientific Research Projects of Young of Binzhou University （BZXYQNLG200725）
