Abstract
A new simple loop algebra M is constructed, which is devoted to the establishing of an isospectral problem. By making use of the Tu scheme, the multi-component Tu hierarchy is obtained. Furthermore, an expanding loop algebra M of the loop algebra M is presented. Based on the M, the multi-component integrable coupling system of the multi-component Tu hierarchy has been worked out. The method can be applied to other nonlinear evolution equation hierarchies.
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