TY - JOUR
T1 - Weakly localized states for nonlinear Dirac equations
AU - Borrelli, William
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - critical Dirac equations
KW - critical Dirac equations
UR - http://hdl.handle.net/10807/171312
U2 - 10.1007/s00526-018-1420-0
DO - 10.1007/s00526-018-1420-0
M3 - Article
SN - 0944-2669
VL - 57
SP - N/A-N/A
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
ER -