Asymptotic stability of solitary waves in generalized Gross--Neveu model

2014/07/02 by Andrew Comech, Comech, Andrew, Tuoc Van Phan +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1407.0606

35 pages, 2 figures

arxiv created 2014/07/03 · arxiv updated 2014/07/07

Abstract

For the nonlinear Dirac equation in (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). The asymptotic stability is proved for initial data in H¹. 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.

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