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Weakly localized states for nonlinear Dirac equations

Borrelli, William (2018), Weakly localized states for nonlinear Dirac equations, Calculus of Variations and Partial Differential Equations, 157, 6, p. article: 155. 10.1007/s00526-018-1420-0

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Calculus of Variations and Partial Differential Equations
Volume
157
Number
6
Publisher
Springer
Pages
article: 155
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Author(s)
Borrelli, William
Abstract (EN)
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.
Subjects / Keywords
mathématiques; nonlinear Dirac equations