The 1-D Dirac equation with concentrated nonlinearity
Mathematical Physics
2016-07-05 v1 math.MP
Abstract
We define and study the Cauchy problem for a 1-D nonlinear Dirac equation with nonlinearities concentrated at one point. Global well-posedness is provided and conservation laws for mass and energy are shown. Several examples, including nonlinear Gesztesy-\v{S}eba models and the concentrated versions of the Bragg Resonance, Gross-Neveu, and Soler type models, all within the scope of the present paper, are given. The key point of the proof consists in the reduction of the original equation to a nonlinear integral equation for an auxiliary, space-independent variable (the "charge").
Cite
@article{arxiv.1607.00665,
title = {The 1-D Dirac equation with concentrated nonlinearity},
author = {Claudio Cacciapuoti and Raffaele Carlone and Diego Noja and Andrea Posilicano},
journal= {arXiv preprint arXiv:1607.00665},
year = {2016}
}
Comments
20 pages