Weakly localized states for nonlinear Dirac equations
Analysis of PDEs
2018-07-31 v2 Mathematical Physics
math.MP
Abstract
We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks to a particular radial ansatz, which also allows to provide the exact asymptotic behavior of spinor components. Moreover, those solutions admit a variational characterization. We also indicate how the content of the present paper allows to extend our previous results for the massive case [5] to more general nonlinearities.
Cite
@article{arxiv.1802.05617,
title = {Weakly localized states for nonlinear Dirac equations},
author = {William Borrelli},
journal= {arXiv preprint arXiv:1802.05617},
year = {2018}
}