Universal character of the discrete nonlinear Schrödinger equation

We address the universal applicability of the discrete nonlinear Schrödinger equation. By employing an original but general top-down-bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely applicable and simplest possible model, revealing that the discrete nonlinear Schrödinger equation is "universally" fit to describe light propagation even in discrete tensorial nonlinear systems and in the presence of nonparaxial and vectorial effects.