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arXiv · 1210.7261

Small amplitude solitary waves in the Dirac-Maxwell system

Andrew Comech·David Stuart
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Abstract

We study nonlinear bound states, or solitary waves, in the Dirac-Maxwell system proving the existence of solutions in which the Dirac wave function is of the form $\phi(x,\omega)e^{-i\omega t}$, $\omega\in(-m,\omega_*)$, with some $\omega_*>-m$, such that $\phi_\omega\in H^1(\mathbb{R}^3,\mathbb{C}^4)$, $\Vert\phi_\omega\Vert^2_{L^2}=O(m-|\omega|)$, and $\Vert\phi_\omega\Vert_{L^\infty}=O(m-|\omega|)$. The method of proof is an implicit function theorem argument based on an identification of the nonrelativistic limit as the ground state of the Choquard equation.

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Andrew Comech, David Stuart. 2012-10-26. Small amplitude solitary waves in the Dirac-Maxwell system. https://arxiv.org/abs/1210.7261

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