THE INTEGRABLE COUPLINGS OF THE GENERALIZED COUPLED mKdV HIERARCHY AND ITS HAMILTONIAN STRUCTURES

We construct a loop algebra 3 , then a new 4×4 isospectral problem is presented. By Tu scheme, the generalized coupled mKdV equation hierarchy is derived. Based on an expanding loop algebra F3 of the loop algebra 3 , the integrable couplings of the generalized coupled mKdV hierarchy is solved. Finally, the Hamiltonian structures of the integrable couplings of the generalized coupled mKdV hierarchy is obtained by the quadratic-form identity.