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On stability of standing waves of nonlinear Dirac equations. (English) Zbl 1251.35098

Summary: 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 in [S. Cuccagna, Commun. Math. Phys. 305, No. 2, 279–331 (2011; Zbl 1222.35183)] for the nonlinear Schrödinger equation, because of the strong indefiniteness of the energy.

MSC:

35Q41 Time-dependent Schrödinger equations and Dirac equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)

Citations:

Zbl 1222.35183
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