The One-Dimensional Dirac Equation With Concentrated Nonlinearity

DOI10.1137/16M1084420zbMath1371.35236arXiv1607.00665OpenAlexW2643561038MaRDI QIDQ5270349

Diego Noja, Raffaele Carlone, Andrea Posilicano, Claudio Cacciapuoti

Publication date: 23 June 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00665

zbMATH Keywords

well-posednesspoint interactionsnonlinear Dirac equation

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (7)

Stability of the standing waves of the concentrated NLSE in dimension two ⋮ Spectral stability and instability of solitary waves of the Dirac equation with concentrated nonlinearity ⋮ Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit ⋮ Blow-up for the pointwise NLS in dimension two: absence of critical power ⋮ Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one ⋮ Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity ⋮ Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one

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