On the integrability of a new discrete nonlinear Schrodinger equation

We consider the nonlinear Schrodinger equation on the lattice introduced by Leon and Manna two years ago to describe the slowly varying envelope approximation of some nonlinear differential difference equations. We show that this equation does not admit local generalized symmetries of order greater than three. In such a way we prove that the Leon and Manna discrete nonlinear Schrodinger equation does not have the same integrability properties as the Toda lattice equation, from which it has been derived. At the end we provide some reasoning to justify the result obtained.