Abstract
We will discuss how to generate integrable couplings from zero curvature equations associated with matrix spectral problems. The key elements are matrix loop algebras consisting of block matrices with blocks of the same size or different sizes. Hamiltonian structures are furnished by applying the variational identity defined over semi-direct sums of Lie algebras. Illustrative examples include integrable couplings of the AKNS hierarchy by using the irreducible representations V2 and V3 of the special linear Lie algebra sl(2,R).
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