{"paper":{"title":"Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Avadh Saxena, Avinash Khare, Franz G. Mertens, Fred Cooper, Niurka R. Quintero, Sihong Shao","submitted_at":"2014-05-21T20:21:40Z","abstract_excerpt":"We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction $ \\frac{g^2}{\\kappa+1} ({\\bar \\Psi} \\Psi)^{\\kappa+1}$ and with mass $m$. Using the exact analytic form for rest frame solitary waves of the form $\\Psi(x,t) = \\psi(x) e^{-i \\omega t}$ for arbitrary $ \\kappa$, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schr\\\"odinger equation. In particular we study the validity of a version of Derrick's theorem, the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5547","kind":"arxiv","version":1},"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"}