Section: Scientific Foundations

Numerical analysis of Schrödinger equations

In collaboration with M. Taki (PhLAM laboratory, Lille), Christophe Besse and Guillaume Dujardin are considering dispersive equations modelling the propagation of a laser beam in an optic fiber. They are trying to explain the possible ways of creating rogue waves in the propagation of laser beams. More generally, they are trying to explain which terms in the dispersive Schrödinger-like equations obtained by the physicists allow which physical behaviour of the solutions (e.g. the creation of rogue waves).

In collaboration with G. Reinish (Nice Observatory), Christophe Besse and Guillaume Dujardin are working on the numerical computation of the ground state and the first bound states of the non linear Schrödinger-Poisson system with confining quadratic potential in 2 space dimension modelling quatum dot helium. The goal is to perform after that numerical time stepping methods to simulate the dynamics of the NLSP system and compute accurately some quantities of physical interest as functions of time.