Weakly localized states for nonlinear Dirac equations

William Borrelli (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

William Borrelli. Weakly localized states for nonlinear Dirac equations. Calculus of Variations and Partial Differential Equations, 2018. ⟨hal-01709328v2⟩