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