1 jun 2016 -- 15:00 [open in google calendar]
Scuola Normale Superiore, Aula Mancini
In this talk, we will be interested in standing wave solutions to a fourth order nonlinear Schrödinger equation having second and fourth order dispersion terms. This kind of equation naturally appears in nonlinear optics. In a first time, we will establish the existence of ground-state solutions. We can obtain them with two different ways : either by imposing a L2 mass constraint or via a Lp constraint. We will then be interested in their qualitative properties : positivity, symmetry, exponential decay, uniqueness and orbital stability. We will conclude with some open questions. Joint work with Denis Bonheure, Ederson Moreira Dos Santos and Robson Nascimento.