On stability of standing waves of nonlinear Dirac equations

Nabile Boussaid (1) , Scipio Cuccagna (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 DMI - Dipartimento di Matematica e Informatica

We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are not able to get the full result proved by Cuccagna for the nonlinear Schrödinger equation, because of the strong indefiniteness of the energy.

Domains: Analysis of PDEs [math.AP]; Mathematical Physics [math-ph]

Nabile Boussaid, Scipio Cuccagna. On stability of standing waves of nonlinear Dirac equations. 2011. ⟨hal-00578790v3⟩