Stability of solitary waves and vortices in a 2D nonlinear Dirac model
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 Schr\"odinger equation.
Keywords
Cite
@article{arxiv.1512.03973,
title = {Stability of solitary waves and vortices in a 2D nonlinear Dirac model},
author = {J. Cuevas-Maraver and P. G. Kevrekidis and A. Saxena and A. Comech and R. Lan},
journal= {arXiv preprint arXiv:1512.03973},
year = {2016}
}
Comments
Includes Supplemental material