A type of expanding integrable system for NLS-mKdV hierarchy

Abstract

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.