Asymptotic stability of solitary waves in generalized Gross-Neveu model

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• 作者：Andrew Comech^a ; ^b ; ^{comech@math.tamu.edu} ; Tuoc Van Phan^c ; ¹ ; Atanas Stefanov^d ; ²
• 关键词：Gross&ndash ; Neveu model ; Nonlinear Dirac equation ; Solitary waves ; Asymptotic stability ; Weighted spaces
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2017
• 出版时间：January-February 2017
• 年：2017
• 卷：34
• 期：1
• 页码：157-196
• 全文大小：663 K
• 卷排序：34

文摘

For the nonlinear Dirac equation in (1+1)D(1+1)D with scalar self-interaction (Gross–Neveu model), with quintic and higher order nonlinearities (and within certain range of the parameters), we prove that solitary wave solutions are asymptotically stable in the “even” subspace of perturbations (to ignore translations and eigenvalues ±2ωi±2ωi). The asymptotic stability is proved for initial data in H1H1. The approach is based on the spectral information about the linearization at solitary waves which we justify by numerical simulations. For the proof, we develop the spectral theory for the linearized operators and obtain appropriate estimates in mixed Lebesgue spaces, with and without weights.