Tri-integrable Couplings by Matrix Loop Algebras

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.