| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 8899161 | Journal of Differential Equations | 2017 | 24 Pages |
Abstract
In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose-Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |Ï|2Ï and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H12(R2,C2)âªL4(R2,C4) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
William Borrelli,