Initial boundary value problem for nonlinear Dirac equation of Gross-Neveu type in 1 + 1 dimensions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.04.058
Abstract: This paper studies an initial boundary value problem for a class of nonlinear Dirac equations with cubic terms and moving boundary. For the initial data with bounded $L^2$ norm and the suitable boundary conditions, the… read more here.
Keywords: initial boundary; value problem; boundary value; nonlinear dirac ... See more keywords
Stability of nonlinear Dirac solitons under the action of external potential.
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DOI: 10.1063/5.0177392
Abstract: The instabilities observed in direct numerical simulations of the Gross-Neveu equation under linear and harmonic potentials are studied. The Lakoba algorithm, based on the method of characteristics, is performed to numerically obtain the two spinor… read more here.
Keywords: stability nonlinear; solitons action; action external; external potential ... See more keywords
Stability of parametrically driven, damped nonlinear Dirac solitons.
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DOI: 10.1063/5.0281726
Abstract: The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the linearization of this… read more here.
Keywords: stability; damped nonlinear; driven damped; stability parametrically ... See more keywords
Length-scale competition in the parametrically driven nonlinear Dirac equation with a spatially periodic force
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ab2469
Abstract: Soliton dynamics in the damped and parametrically driven nonlinear Dirac equation, in 1 + 1 dimension with scalar–scalar self-interaction is analysed. The considered parametric force has the spatial period . A variational approach using collective… read more here.
Keywords: nonlinear dirac; dirac equation; soliton; force ... See more keywords
Nonlinear Dirac Cones
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DOI: 10.1103/physrevb.96.121406
Abstract: Physics arising from two-dimensional~(2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such $2$D Dirac cones are often characterized… read more here.
Keywords: dirac cones; phase; nonlinear dirac; berry phase ... See more keywords
Potential well and multiplicity of solutions for nonlinear Dirac equations
Sign Up to like & getrecommendations! Published in 2020 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2020028
Abstract: In this paper we consider the semi-classical solutions of a massive Dirac equations in presence of a critical growth nonlinearity \begin{document}$ -i\hbar \sum\limits_{k = 1}^{3}\alpha_k\partial_k w+a\beta w+V(x)w = f(|w|)w. $\end{document} Under a local condition imposed… read more here.
Keywords: nonlinear dirac; multiplicity solutions; dirac equations; potential well ... See more keywords