Two Types of Coupling Integrable Couplings of the S-mKdV Hierarchy

第一， 4 谎言代数学被构造。然后，循环代数学的应用程序被介绍获得由使用 Tu 计划联合 S-mKdV 层次的 integrable couplings 的二种类型。S-mKdV 层次的联合 integrable couplings 在纸还原剂获得了到 mKdV 方程的联合 integrable couplings 和非线性的 Schr 的联合 integrable couplings ? dinger 方程分别地。在纸给的方法能通常习惯于另外的层次。

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.