Abstract
Abstract We create a class of non-semisimple matrix loop algebras, and use the associated zero curvature equations to construct tri-integrable couplings. An application is made for the AKNS equations as an illustrative example. Hamiltonian structures of the resulting tri-integrable couplings are furnished by the variational identities over the presented matrix loop algebras, which implies the commutativity of the sequences of symmetries and conserved functionals.
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