The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions

A new loop algebra G˜M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component coupled Burgers hierarchy is obtained. Furthermore, an expanding loop algebra F˜M of the loop algebra G˜M is presented. It follows that the multi-component integrable coupling system of the multi-component coupled Burgers hierarchy is worked out. In general, the method can be applied to other evolution equations hierarchies.