The coupling integrable couplings of the generalized coupled Burgers equation hierarchy and its Hamiltonian structure

Abstract

In this paper, we mainly give the Lie algebras E, F and H of three kinds and their commutator, respectively. Next, we establish three isospectral problems with the help of their corresponding loop algebras Ẽ, F̃, and H̃. Based on on the Tu scheme, coupling integrable couplings of three kinds for the generalized coupled Burgers equation hierarchy are obtained. Finally, we obtain the Hamiltonian structure of one of the coupling integrable couplings of the generalized coupled Burgers equation hierarchy by using the quadratic-form identity.