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
TypeArticle accepté pour publication ou publié
Journal nameCalculus of Variations and Partial Differential Equations
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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  to more general nonlinearities.
Subjects / Keywordsmathématiques; nonlinear Dirac equations
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An overview on the standing waves of nonlinear Schroedinger and Dirac equations on metric graphs with localized nonlinearity Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo (2019) Document de travail / Working paper