The integrable couplings of the Modified Jaulent-Miodek hierarchy and its Hamiltonian structure

A new higher-dimensional matrix isospectral problem is proposed to construct the integrable couplings of the Modified Jaulent-Miodek (MJM) hierarchy. The Hamiltonian structure of the integrable couplings of the MJM hierarchy is worked out by a proper linear isomorphic map and the quadratic-form identity.