""We consider the classi\\fcation up to a Mobious transformation of real linearizable and integrable difference equations with dispersion defi\\fned on a square lattice by the multiscale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions. are insufficient for a complete characterization of the subclass of multilinear equations on the square lattice""
R., H.H., Levi, D., Scimiterna, C. (2012). Classification of discrete systems on a square lattice. THEORETICAL AND MATHEMATICAL PHYSICS, 172(2), 1097-1108.