We define and study the Cauchy problem for a one-dimensional (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--Šeba models and the concentrated versions of the Bragg resonance and 1-D Soler (also known as massive Gross--Neveu) 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 One-Dimensional Dirac Equation With Concentrated Nonlinearity / Cacciapuoti, Claudio; Carlone, Raffaele; Noja, DIEGO DAVIDE RAFFAELE; Posilicano, Andrea. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 49:3(2017), pp. 2246-2268. [10.1137/16M1084420]
The One-Dimensional Dirac Equation With Concentrated Nonlinearity
CACCIAPUOTI, CLAUDIO;CARLONE, RAFFAELE;NOJA, DIEGO DAVIDE RAFFAELE;POSILICANO, ANDREA
2017
Abstract
We define and study the Cauchy problem for a one-dimensional (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--Šeba models and the concentrated versions of the Bragg resonance and 1-D Soler (also known as massive Gross--Neveu) 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.| File | Dimensione | Formato | |
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