Asymptotic stability of small gap solitons in nonlinear Dirac equations (Q2865546)
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scientific article; zbMATH DE number 6234889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic stability of small gap solitons in nonlinear Dirac equations |
scientific article; zbMATH DE number 6234889 |
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Asymptotic stability of small gap solitons in nonlinear Dirac equations (English)
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29 November 2013
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Nonlinear Dirac equation
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Asymptotic stability
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Small gap solutions
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Solitary waves
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Strichartz estimates
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0.9307278
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0.9093033
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0.9078771
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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 \textit{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.
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