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On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential. (English) Zbl 1334.35264

Summary: We consider a Dirac operator with short range potential and with eigenvalues. We add a nonlinear term and we show that the small standing waves of the corresponding nonlinear Dirac equation (NLD) are attractors for small solutions of the NLD. This extends to the NLD results already known for the Nonlinear Schrödinger Equation (NLS).

MSC:

35Q41 Time-dependent Schrödinger equations and Dirac equations
35B32 Bifurcations in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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