Lax pair, cyclic basis, and a new integrable system

A direct approach to zero-curvature representation, as introduced by Marvan is applied to generate a new class of integrable equations by starting with the generic Lax operator (x-part) for a coupled set of nonlinear equations. The class of equation so obtained is more general than those usually obtained with the help of standard recursion operator. Finally some particular type of equations are identified by the special choice of the arbitrary functions occurring in the final solution of the time part of the Lax equation. The methodology is specially useful when the x-part of the Lax operator does not contain any spectral parameter