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arXiv · 1607.00665

The 1-D Dirac equation with concentrated nonlinearity

Claudio Cacciapuoti·Raffaele Carlone·Diego Noja·Andrea Posilicano
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Abstract

We define and study the Cauchy problem for a 1-D nonlinear Dirac equation with nonlinearities concentrated at one point. Global well-posedness is provided and conservation laws for mass and energy are shown. Several examples, including nonlinear Gesztesy-\v{S}eba models and the concentrated versions of the Bragg Resonance, Gross-Neveu, and Soler type models, all within the scope of the present paper, are given. The key point of the proof consists in the reduction of the original equation to a nonlinear integral equation for an auxiliary, space-independent variable (the "charge").

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Claudio Cacciapuoti, Raffaele Carlone, Diego Noja, Andrea Posilicano. 2016-07-03. The 1-D Dirac equation with concentrated nonlinearity. https://arxiv.org/abs/1607.00665

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