Stability of Solitary Waves and Vortices in a 2D Nonlinear Dirac Model.
We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These conclusions are found not to be restricted to the case of cubic two-dimensional nonlinearities but are found to be extended to the case of quintic nonlinearity, as well as to that of three spatial dimensions. Our results also reveal nontrivial differences with respect to the better understood nonrelativistic analogue of the model, namely the nonlinear Schrödinger equation.
Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla. Escuela Politécnica Superior, C/ Virgen de África, 7, 41011 Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012 Sevilla, Spain.
Jesús
J
Cuevas-Maraver
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.|Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Panayotis G
PG
Kevrekidis
Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Avadh
A
Saxena
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368, USA.|Institute for Information Transmission Problems, Moscow 127994, Russia.
Andrew
A
Comech
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368, USA.
Ruomeng
R
Lan