{"paper":{"title":"Small amplitude solitary waves in the Dirac-Maxwell system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Andrew Comech, David Stuart","submitted_at":"2012-10-26T22:13:04Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7261","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}