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arXiv · 1512.03973

Stability of solitary waves and vortices in a 2D nonlinear Dirac model

J. Cuevas-Maraver·P. G. Kevrekidis·A. Saxena·A. Comech·R. Lan
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Abstract

We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions consisting of a soliton in one component and a vortex in the other to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These results pave the way for a systematic stability and dynamics analysis of higher dimensional waveforms in a broad class of nonlinear Dirac models and a comparison revealing nontrivial differences with respect to their better understood non-relativistic analogue, the nonlinear Schrödinger equation.

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J. Cuevas-Maraver, P. G. Kevrekidis, A. Saxena, A. Comech, R. Lan. 2016-04-24. Stability of solitary waves and vortices in a 2D nonlinear Dirac model. https://doi.org/10.1103/physrevlett.116.214101

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