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Pré-Publication, Document De Travail Année : 2018

NONLINEAR DIRAC EQUATION ON GRAPHS WITH LOCALIZED NONLINEARITIES: BOUND STATES AND NONRELATIVISTIC LIMIT

Résumé

In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the bound states (arising as critical points of the NLD action functional) and we prove that, in the L 2-subcritical case, they converge to the bound states of the NLS equation in the nonrelativistic limit.
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Dates et versions

hal-01842039 , version 1 (17-07-2018)

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William Borrelli, Raffaele Carlone, Lorenzo Tentarelli. NONLINEAR DIRAC EQUATION ON GRAPHS WITH LOCALIZED NONLINEARITIES: BOUND STATES AND NONRELATIVISTIC LIMIT. 2018. ⟨hal-01842039⟩
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