Singularities in optical extended systems

We will present our experience on applying discrete group theory arguments to
study the nonlinear Schrödinger equation. First, we will present the angular
pseudomomentum theory, i.e., a set of results that allows to classify and
predict some properties of the stationary solutions of such equation with
discrete rotational
symmetry. Next, we will use these arguments to study the
dynamical evolution of symmetrical solutions. Finally, we will use all this
knowledge in the study of the dynamical behaviour of phase singularities of an
optical field, a topic that is commonly enclosed in a separated branch of
optics called "nonlinear singular optics".