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Inaugural Conference of the Fibonacci Laboratory

On the Stability of Standing Waves of the Dirac Equation

speaker: Scipio Cuccagna (Università di Trieste)

abstract: The classical variational methods used to prove stability of standing waves of dispersive equations do not work for the Dirac equation because of the strong indefiniteness of the energy. Here we report on joint work with N.Boussaid and we show that methods based on dispersion of the continuous modes, originally designed for the Nonlinear Schroedinger equation, partially work for the Dirac equation. While the results are partial and conditional on a certain number of hypotheses, there is a scheme which allows to frame the problem. In particular energy indefiniteness plays a role and clouds the picture, but in a way somewhat technical and that can be overcome at least in special situations.

Tue 6 Mar, 17:25 - 18:25, Sala Azzurra
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