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- Å eba 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
Cacciapuoti, C., Carlone, R., Noja, D., Posilicano, A. (2017). The one-dimensional Dirac equation with concentrated nonlinearity. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 49(3), 2246-2268 [10.1137/16M1084420].
The one-dimensional Dirac equation with concentrated nonlinearity
NOJA, DIEGO DAVIDEPenultimo
;
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- Å eba 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
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