# On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆

Mathematical Modelling of Natural Phenomena (2012)

- Volume: 7, Issue: 2, page 13-31
- ISSN: 0973-5348

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topBerkolaiko, G., and Comech, A.. "On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆." Mathematical Modelling of Natural Phenomena 7.2 (2012): 13-31. <http://eudml.org/doc/222290>.

@article{Berkolaiko2012,

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.},

author = {Berkolaiko, G., Comech, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {nonlinear Dirac equation; Dirac operator; spectral stability; linear instability; solitary waves; Soler model; massive Gross-Neveu model; Jost solution; Evans function},

language = {eng},

month = {2},

number = {2},

pages = {13-31},

publisher = {EDP Sciences},

title = {On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆},

url = {http://eudml.org/doc/222290},

volume = {7},

year = {2012},

}

TY - JOUR

AU - Berkolaiko, G.

AU - Comech, A.

TI - On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆

JO - Mathematical Modelling of Natural Phenomena

DA - 2012/2//

PB - EDP Sciences

VL - 7

IS - 2

SP - 13

EP - 31

AB - 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.

LA - eng

KW - nonlinear Dirac equation; Dirac operator; spectral stability; linear instability; solitary waves; Soler model; massive Gross-Neveu model; Jost solution; Evans function

UR - http://eudml.org/doc/222290

ER -

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