An Algebraic Structure of Zero Curvature Representations Associated With Coupled Integrable Couplings and Applications to τ-Symmetry Algebras

We establish an algebraic structure for zero curvature representations of coupled integrable couplings. The adopted zero curvature representations are associated with Lie algebras possessing two sub-Lie algebras in form of semi-direct sums of Lie algebras. By applying the presented algebraic structures to the AKNS systems, we give an approach for generating τ-symmetry algebras of coupled integrable couplings