Intervenant : VAN DEN BOSCH Hanne (Universidad de Chile)
Solitary waves in Nonlinear Dirac Equations
Colloquium (suivi d'un pot)
Le : 04/10/2022 de : 15h30: à : 16h30:
In nonlinear dispersive equations, the competition between the linear dispersion and nonlinear self-interaction gives rise to localized solutions that maintain their shape as time evolves. Famous examples of this are the solitons in the Korteweg-de Vries equation or solitary waves for the nonlinear Schrödinger equation. In the latter case, there is a beautiful theory to determine if small perturbations in the initial condition remain close to a solitary wave as time evolves, or on the contrary, may completely destroy its shape. In many types of Nonlinear Dirac equations, these special solutions exist as well, but very little is known rigorously about their properties. During the colloquium, I will present this problem and compare the results for the Schrödinger case with those for their Dirac analogues.
Salle : A709