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.

Borrelli, W., Weakly localized states for nonlinear Dirac equations, <<CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS>>, 2018; 57 (6): N/A-N/A. [doi:10.1007/s00526-018-1420-0] [http://hdl.handle.net/10807/171312]

Weakly localized states for nonlinear Dirac equations

Borrelli, W.
2018

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.
Inglese
Borrelli, W., Weakly localized states for nonlinear Dirac equations, <<CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS>>, 2018; 57 (6): N/A-N/A. [doi:10.1007/s00526-018-1420-0] [http://hdl.handle.net/10807/171312]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/171312
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