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.

26 pages, no figures

References in corpus (3)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$
• Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases

Cited by in corpus (2)

• Survey on global existence in the nonlinear Dirac equations in one dimension
• On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation