We derive exact analytic solutions of nonlinear Dirac equations with Kerr-like cubic nonlinearity. The equations model, among many physical systems, a Bose-Einstein condensate confined by a two-dimensional honeycomb optical lattice as well as relativistic solitons in optical waveguide arrays. The nonrelativistic limit of the solutions is derived, and the role of the nonlinearity on localization is discussed. The possibility of realizing some of these solutions in waveguide arrays and Bose-Einstein condensates is pointed out.
|Physical Review A - Atomic, Molecular, and Optical Physics
|Published - Nov 10 2014
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics