The fractional nonlinear Schrödinger equation. Modelling, theory and numerical approximation

In this talk several issues of the fractional nonlinear Schrödinger equation are analysed. Some properties of the equation enable the use of Concentration-Compactness theory to prove the existence of solitary wave solutions with algebraic decay. Then a numerical approach introduces a full discretization of the periodic initial-value problem and derives error estimates. From the numerical generation of the solitary wave profiles and the fully discrete scheme, a computational study of the dynamics of the solitary waves is developed. This is a joint work with Nuria Reguera.