Asymptotic stability of small gap solitons in the nonlinear Dirac equations

Abstract

We prove dispersive decay estimates for the one-dimensional Dirac operator and use them to prove asymptotic stability of small gap solitons in the nonlinear Dirac equations with quintic and higher-order nonlinear terms.

arXiv comment26 pages, no figures

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Cited by in corpus (5)

• Numerical methods for nonlinear Dirac equation
• Survey on global existence in the nonlinear Dirac equations in one dimension
• On the meaning of the Vakhitov-Kolokolov stability criterion for the nonlinear Dirac equation
• On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation
• On stability of standing waves of nonlinear Dirac equations