The integrable couplings of the generalized coupled Burgers hierarchy and its Hamiltonian structures

We construct a loop algebra A3∼, then a new 4 × 4 isospectral problem is presented. By making use of Tu scheme, the generalized coupled Burgers equation hierarchy is derived. Based on an expanding loop algebra F3∼ of the loop algebra A3∼, the integrable couplings of the generalized coupled Burgers hierarchy is worked out. Finally, the Hamiltonian structures of the integrable couplings of the generalized coupled Burgers hierarchy is obtained by the quadratic-form identity.