Cuevas-Maraver, JesúsKevrekidis, Panayotis G.Aceves, A. B.Saxena, Avadh2017-09-282017-09-282017Cuevas-Maraver, J., Kevrekidis, P.G., Aceves, A.B. y Saxena, A. (2017). Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum. Journal of Physics A: Mathematical and Theoretical, 1-13.1751-81131751-8121http://hdl.handle.net/11441/64852In 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1088/17518121/aa8e36