Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D

DOI10.1016/j.physleta.2017.11.032zbMath1387.35553OpenAlexW2772113134MaRDI QIDQ1700537

T. I. Lakoba

Publication date: 6 March 2018

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2017.11.032

zbMATH Keywords

method of characteristicssplit-step methodnonlinear Dirac equationmassive Gross-Neveu modelsolitary wave stability

Mathematics Subject Classification ID

Model quantum field theories (81T10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (10)

High-order conservative schemes for the nonlinear Dirac equation ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. I: Periodic boundary conditions ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. II: Nonreflecting boundary conditions ⋮ Results on the spectral stability of standing wave solutions of the Soler model in 1-D ⋮ Study of instability of the Fourier split-step method for the massive Gross-Neveu model ⋮ Spinor solitons and their \(\mathcal{PT}\)-symmetric offspring ⋮ Nonexistence of self-similar blowup for the nonlinear Dirac equations in \((1+1)\) dimensions ⋮ Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction ⋮ Integrable semi-discretization of the massive Thirring system in laboratory coordinates ⋮ Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity

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