Special Session 37: Nonlinear elliptic problems in geometry and physics

Standing wave and travelling wave solutions for a fourth order Schroedinger equation

Jean-Baptiste Casteras
University of Lisbon
Portugal
Co-Author(s):    
Abstract:
In this talk, we will be interested in standing wave solutions to a fourth order nonlinear Schroedinger 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 and renormalized solutions. We will then be interested in their qualitative properties, in particular their stability.