{"paper":{"title":"Solitary wave in the Nonlinear Dirac Equation with arbitrary nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math.MP","nlin.PS"],"primary_cat":"math-ph","authors_text":"Avadh Saxena, Avinash Khare, Bogdan Mihaila, Fred Cooper","submitted_at":"2010-07-19T16:09:02Z","abstract_excerpt":"We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\\frac{g^2}{k+1} ({\\bar \\Psi} \\Psi)^{k+1}$, as well as a vector-vector self interaction $\\frac{g^2}{k+1} ({\\bar \\Psi} \\gamma_\\mu \\Psi \\bPsi \\gamma^\\mu \\Psi)^{\\frac{1}{2}(k+1)}$. We find the exact analytic form for solitary waves for arbitrary $k$ and find that they are a generalization of the exact solutions for the nonlinear Schr\\\"odinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. We perform the nonrelativistic reduction and find the $1/2m$ correc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3194","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"}