Weakly localized states for nonlinear Dirac equations |
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Authors: | Email author" target="_blank">William?BorrelliEmail author |
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Institution: | 1.Université Paris-Dauphine, PSL Research University, CNRS, UMR 7534, CEREMADE,Paris,France |
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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 as least action critical points of a suitable action functional. 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. |
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