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
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