{"paper":{"title":"Linear instability of nonlinear Dirac equation in 1D with higher order nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Andrew Comech","submitted_at":"2012-03-17T12:51:33Z","abstract_excerpt":"We consider the nonlinear Dirac equation in one dimension, also known as the Soler model in (1+1) dimensions, or the massive Gross-Neveu model: $i\\partial_t\\psi=-i\\alpha\\partial_x\\psi+m\\beta\\psi-f(\\psi^\\ast\\beta\\psi)\\beta\\psi$, $\\psi(x,t)\\in\\C^2$, $x\\in\\R$, $f\\in C^\\infty(\\R)$, $m>0$, where $\\alpha$, $\\beta$ are $2\\times 2$ hermitian matrices which satisfy $\\alpha^2=\\beta^2=1$, $\\alpha\\beta+\\beta\\alpha=0$.\n  We study the spectral stability of solitary wave solutions $\\phi_\\omega(x)e^{-i\\omega t}$. More precisely, we study the presence of point eigenvalues in the spectra of linearizations at so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3859","kind":"arxiv","version":2},"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"}