Integrable nonlinear field equations and loop algebra structures

We apply the (direct and inverse) prolongation method to a couple of non-linear Schrödinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system under consideration, we develop a procedure with allows us to generate a new class of integrable non-linear field equations containing the original ones as a special case.