2019-05-212019-05-212018Cuevas-Maraver, J., Boussaïd, N.,...,Saxena, A. (2018). Solitary waves in the Nonlinear Dirac Equation. En Nonlinear Systems, Vol. 1. Mathematical Theory and Computational Methods (pp. 89-143). Switzerland: Springer Nature Switzerland AG978-3-319-66765-2978-3-319-66766-9https://hdl.handle.net/11441/86611In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associ- ated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical per- spective and then complemented with numerical computations. Finally, the dynam- ics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr¨odinger equation.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 InternacionalAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/SolitonsSolitary wavesVorticesNonlinear Dirac equationStabilitySoler modelinfo:eu-repo/semantics/bookPartinfo:eu-repo/semantics/openAccess10.1007/978-3-319-66766-9_4