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Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum

 

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Opened Access Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
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Author: Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
Aceves, A. B.
Saxena, Avadh
Coordinator/Director: Archilla, Juan F. R.
Department: Universidad de Sevilla. Departamento de Física I
Date: 2017
Document type: Article
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.
Size: 4.709Mb
Format: PDF

URI: http://hdl.handle.net/11441/64852

DOI: 10.1088/17518121/aa8e36

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

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