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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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
35C07 Traveling wave solutions
35B35 Stability in context of PDEs

Citations:

Zbl 1175.35138
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References:

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