{"paper":{"title":"On linear instability of solitary waves for the nonlinear Dirac equation","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, Meijiao Guan, Stephen Gustafson","submitted_at":"2012-09-05T23:43:22Z","abstract_excerpt":"We consider the nonlinear Dirac equation, also known as the Soler model: $i\\p\\sb t\\psi=-i\\alpha \\cdot \\nabla \\psi+m \\beta \\psi-f(\\psi\\sp\\ast \\beta \\psi) \\beta \\psi$, $\\psi(x,t)\\in\\mathbb{C}^{N}$, $x\\in\\mathbb{R}^n$, $n\\le 3$, $f\\in C\\sp 2(\\R)$, where $\\alpha_j$, $j = 1,...,n$, and $\\beta$ are $N \\times N$ Hermitian matrices which satisfy $\\alpha_j^2=\\beta^2=I_N$, $\\alpha_j \\beta+\\beta \\alpha_j=0$, $\\alpha_j \\alpha_k + \\alpha_k \\alpha_j =2 \\delta_{jk} I_N$. We study the spectral stability of solitary wave solutions $\\phi(x)e^{-i\\omega t}$. We study the point spectrum of linearizations at solita"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1146","kind":"arxiv","version":3},"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"}