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On Spectral Stability of Solitary Waves of Nonlinear DiracEquation in 1D⋆⋆

Published online by Cambridge University Press:  29 February 2012

G. Berkolaiko  and
A. Comech
G. Berkolaiko
Affiliation:
Mathematics Department, Texas A&M University, College Station, TX 77843, USA
A. Comech*
Affiliation:
Mathematics Department, Texas A&M University, College Station, TX 77843, USA Institute for Information Transmission Problems, Moscow 101447, Russia
*
⋆ Corresponding author. E-mail: comech@math.tamu.edu
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Abstract

We study the spectral stability of solitary wave solutions to the nonlinear Diracequation in one dimension. We focus on the Dirac equation with cubic nonlinearity, knownas the Soler model in (1+1) dimensions and also as the massive Gross-Neveu model.Presented numerical computations of the spectrum of linearization at a solitary wave showthat the solitary waves are spectrally stable. We corroborate our results by findingexplicit expressions for several of the eigenfunctions. Some of the analytic results holdfor the nonlinear Dirac equation with generic nonlinearity.

Keywords

nonlinear Dirac equationDirac operatorspectral stabilitylinear instabilitysolitary wavesSoler modelmassive Gross-Neveu modelJost solutionEvans function
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 2: Solitary waves , 2012 , pp. 13 - 31
Copyright
© EDP Sciences, 2012

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