Authors: Rafael Hernandez Heredero ¹; Decio Levi ²; Christian Scimiterna ³

• 1 Universidad Politécnica de Madrid
• 2 Università degli Studi Roma Tre = Roma Tre University
• 3 Istituto di Istruzione Superiore Sansi-Leonardi-Volta, Spoleto

In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which seem to be new, depending at most on 2 parameters.