【摘要】 首先构造了loop代数A～2 的一个新的子代数 ,设计了一个等谱问题 .应用屠格式求出了著名的AKNS方程族的一类扩展可积模型 ,即可积耦合 .然后将这种求可积耦合的方法一般化 ,可用于一大类方程族 ,如KN族、GJ族、WKI族等谱系的可积耦合 .提出的方法具有普遍应用价值 .最后作为AKNS方程族的特例 ,求得了KdV方程和MKdV方程的可积耦合更多还原

【Abstract】 First of all, a new subalgebra of loop algebra A～ 2 is constructed. Designing an isospectral problem and using Tu-model we obtain a family of expanding integrable models of the well-known AKNS hierarchy of equations, i.e.integrable couplings. Then the generalized form of the method for obtaining integrable couplings is established. It follows that the integrable couplings for a large kinds of hierarchies of equations, such as KN hierarchy, GJ hierarchy, WKI hierarchy etc. admit this approach. Therefore, the method proposed in this paper has practical values. Finally, as special cases, the integrable couplings of KdV equation and MKdV equation are obtained.更多还原