一类S-mKdV方程族及其扩展可积模型

由loop代数的一个子代数出发，构造了一个线性等谱问题，再利用屠格式计算出了一类Liouvelle意义下的可积系统及其双Hamilton结构，作为该可积系统的约化，得到了著名的Schrdinger方程和mKdV方程，因此称该系统为S-mKdV方程族.根据已构造的的子代数，又构造了维数为5的loop代数的一个新的子代数，由此出发设计了一个线性等谱形式，再利用屠格式求得了S-mKdV方程族的一类扩展可积模型.利用这种方法还可以求BPT方程族、TB方程族等谱系的扩展可积模型.因此本方法具有普遍应用价值.最后作为特例，求得了著名的Schrdinger方程和mKdV方程的可积耦合系统.

A family of S-mKdV hierarchy of equations and its expanding integrable models

Starting from a subalgebra of loop algebra 1 we construct a linear isospectral problem.A type of Liouville integrable system and its bi-Hamiltonian structure are presented by the use of Tu-model again.The reductions to the integrable system give rise to the well-known Schrdinger equation and mKdV equation.Therefore,the system is called S-mKdV hierarchy.In terms of the subalgebra of A constructed,we also construct a new subalgebra G of loop algebra A with five dimensions,from which a linear isospectral form is designed.Again,using Tu-model one obtains a type of expanding integrable models of the S-mKdV hierarchy.Some expanding integrable models of hierarchies,such as BPT hierarchy,TB hierarchy etc.are also obtained by using this method.Hence,the method proposed in this paper has important applications generally.Finally as special cases,the integrable couplings of the well-known Schrdinger equation and mKdV equation are obtained.