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We study the spectral stability of solitary wave solutions $\\phi(x)e^{-i\\omega t}$. We study the point spectrum of linearizations at solita"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.1146","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-05T23:43:22Z","cross_cats_sorted":["math-ph","math.MP","math.SP","nlin.PS"],"title_canon_sha256":"20f6166b324690e97369b6f6ff70717da5b63b00d71a7306143b2046b53d4205","abstract_canon_sha256":"ae711c691ba002baf7ba951f34265b3b88d7e3b3a5eb2e952241634a2883858f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:58.753297Z","signature_b64":"WUTjV2FeaMGfI5Ensy9VMcZWSuzl4uGVB0nuXeuasq2wiEZ2wTSdxybHFIVYR2CJ2vzbmoJWvbk/i+X69rg5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d903833e45fb5689b9a7b3b2a8054a349b2e2f955e293b3abea3515fc486ef1","last_reissued_at":"2026-05-18T03:20:58.752642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:58.752642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\phi(x)e^{-i\\omega t}$. 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