Artículo
Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
Autor/es | Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G. Aceves, A. B. Saxena, Avadh |
Departamento | Universidad de Sevilla. Departamento de Física I |
Fecha de publicación | 2017 |
Fecha de depósito | 2017-09-28 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | MAT2016-79866-R |
Cita | Cuevas-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. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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JPA_cuevas_2017_solitarywaves.pdf | 4.709Mb | [PDF] | Ver/ | |