一类NLS-mKdV方程族的扩展可积系统

利用代数变换，构造了与文献［５］中的loop代数₂的子代数等价的loop代数1的一个子 代数₁.再将₁扩展为一个高维的loop代数.利用设计了一个等谱问题 ，结合子代数间的直 和运算和同构关系，得到了NLS_mKdV方程族的一类扩展可积系统.作为约化情形，求得了著 名的Schrdinger方程与mKdV方程的可积耦合系统. 关键词： loop代数 可积系统 等谱问题

A type of expanding integrable system for NLS-mKdV hierarchy

A subalgerbra ₁, which is equivalent to the subalgebra of the loop al gebra ₂ in “1997 Acta Math. Sin. 40 801”, is constructed by making use of algebraic t ransformation. Then a high-dimensional loop algebra is presented in terms of 1. An isospectral problem is established following by the use of direc t sum ope rators and isomorphic relations among subalgebras. It follows that a type of exp anding integrable system for the NLS_mKdV hierarchy of evolution equations is ob tained. As in reduction cases, the integrable couplings of the famous Schrding er equation and mKdV equation are presented.