Asymptotic stability of small gap solitons in nonlinear Dirac equations. (English) Zbl 1279.35083
The paper under review deals with the asymptotic stability of solitary waves in the nonlinear one-dimensional Dirac equations. Precisely, estimates of Strichartz type are derived by making use of these already obtained by T. Mizumachi in [J. Math. Kyoto Univ. 48, No. 3, 471–497 (2008; Zbl 1175.35138)]. The balance between Strichartz and Mizumachi estimates allows the authors to control both the nonlinear terms and the modulation equations for small gap solitons and thus to prove their asymptotic stability for the nonlinear Dirac equations with quintic and higher-order nonlinear terms.
Reviewer: Dian K. Palagachev (Bari)
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 35C07 | Traveling wave solutions |
| 35B35 | Stability in context of PDEs |
Keywords:
Nonlinear Dirac equation; Asymptotic stability; Small gap solutions; Solitary waves; Strichartz estimatesCitations:
Zbl 1175.35138References:
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