| Issue |
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
|
|
|---|---|---|
| Page(s) | 13 - 31 | |
| DOI | https://doi.org/10.1051/mmnp/20127202 | |
| Published online | 29 February 2012 | |
On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆
1
Mathematics Department, Texas A&M
University, College
Station, TX
77843,
USA
2
Institute for Information Transmission Problems,
Moscow
101447,
Russia
⋆ Corresponding author. E-mail: comech@math.tamu.edu
We study the spectral stability of solitary wave solutions to the nonlinear Dirac equation in one dimension. We focus on the Dirac equation with cubic nonlinearity, known as 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 show that the solitary waves are spectrally stable. We corroborate our results by finding explicit expressions for several of the eigenfunctions. Some of the analytic results hold for the nonlinear Dirac equation with generic nonlinearity.
Mathematics Subject Classification: 35B35 / 37K40 / 65L07 / 81Q05
Key words: nonlinear Dirac equation / Dirac operator / spectral stability / linear instability / solitary waves / Soler model / massive Gross-Neveu model / Jost solution / Evans function
© EDP Sciences, 2012
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