A new multi-component matrix loop algebra and a multi-component integrable couplings of the NLS-MKdV hierarchy and its Hamiltonian structure

A new multi-component matrix loop algebra is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component integrable couplings of the NLS-MKdV hierarchy is obtained, then the bi-Hamiltonian structure of the above system is given.