Universal character of the discrete nonlinear Schrödinger equation

Abstract

We address the universal applicability of the discrete nonlinear Schroedinger 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 Schroedinger equation is 'universally' fit to describe light propagation even in discrete tensorial nonlinear systems and in the presence of nonparaxial and vectorial effects.