On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D Academic Article

abstract

• 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. EDP Sciences, 2012.

authors

• Berkolaiko, Gregory
• Comech, Andrew

published proceedings

• MATHEMATICAL MODELLING OF NATURAL PHENOMENA

author list (cited authors)

• Berkolaiko, G., & Comech, A.

citation count

• 30

complete list of authors

• Berkolaiko, G||Comech, A

publication date

• March 2012

publisher

• EDP Sciences  Publisher

published in

• Mathematical Modelling of Natural Phenomena (MMNP)  Journal

keywords

• Dirac Operator
• Evans Function
• Jost Solution
• Linear Instability
• Massive Gross-neveu Model
• Nonlinear Dirac Equation
• Soler Model
• Solitary Waves
• Spectral Stability

Digital Object Identifier (DOI)

• 10.1051/mmnp/20127202

URI

• https://hdl.handle.net/1969.1/181912

start page

• 13

end page

• 31

volume

• 7

issue

• 2

URL

• http://dx.doi.org/10.1051/mmnp/20127202