Abstract: In this paper, a new
loop algebra is
first constructed, whose commutation operation defined by us accords with that
in the loop algebra Then
by taking advantage of a
new isospectral problem is established, and the multi-component NLS-MKDV
hierarchy is obtained. Finally, an expanded loop algebra of
the loop algebra is
presented. Based on the the
multi-component integrable couplings system of the multi-component NLS-MKDV
hierarchy has been worked out. The loop algebra can
be applied to other nonlinear evolution equations hierarchies.
Keywords and phrases: loop algebra, NLS-MKDV hierarchy, integrable couplings system.
