Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
Abstract
In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum perspective as well as from a highly discrete one. Starting from the former, we see that the continuum Dirac solitons can be continued for all values of the discretization (coupling) parameter, down to the uncoupled (so-called anti-continuum) limit where they result in a 9-site configuration. We also consider configurations with 1- or 2-sites at the anti-continuum limit and continue them to large couplings, finding that they also persist. For all the obtained solutions, we examine not only the existence, but also the spectral stability through a linearization analysis and finally consider prototypical examples of the dynamics for a selected number of cases for which the solutions are found to be unstable.
Keywords
Cite
@article{arxiv.1703.00679,
title = {Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum},
author = {J. Cuevas-Maraver and P. G. Kevrekidis and A. B. Aceves and A. Saxena},
journal= {arXiv preprint arXiv:1703.00679},
year = {2017}
}