Non-Semisimple Lie Algebras of Block Matrices and Applications to Bi-Integrable Couplings

We propose a class of non-semisimple matrix loop algebras consisting of 3×3 block matrices, and form zero curvature equations from the presented loop algebras to generate bi-integrable couplings. Applications are made for the AKNS soliton hierarchy and Hamiltonian structures of the resulting integrable couplings are constructed by using the associated variational identities.