2015/12/31 by J. Cuevas-Maraver, P. G. Kevrekidis, A. Saxena +2 · 2 citations
Physics and Astronomy · #nlin.PS
paper · pdf · doi:10.1103/physrevlett.116.214101
published as Phys. Rev. Lett. 116, 214101 (2016) · Includes Supplemental material
arxiv created 2016/04/24 · arxiv updated 2016/06/01
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.