{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TFK3TEJRAP3YLAS2WRI3HZLQOA","short_pith_number":"pith:TFK3TEJR","schema_version":"1.0","canonical_sha256":"9955b9913103f785825ab451b3e570700c3ec6653419914e36df8674468fa74c","source":{"kind":"arxiv","id":"1203.3859","version":2},"attestation_state":"computed","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"},"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":"1203.3859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-17T12:51:33Z","cross_cats_sorted":["math-ph","math.MP","math.SP","nlin.PS"],"title_canon_sha256":"4e7278e8037ceb26105185c37644e984288a8721a3147c40364fbc759403ca1d","abstract_canon_sha256":"a5452f94c9b39e5eba045fd85d447abcea6e2112688bf0c7a206dae8ab4756af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:01.900192Z","signature_b64":"HxLZ8GjuyQ4cDe1guF3H34Jw1UTG5DdpiN6Q0OQGFUfHFEwC/TDXh0kkhrb8bLilh31P68y4bXW4Qi82gy+hCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9955b9913103f785825ab451b3e570700c3ec6653419914e36df8674468fa74c","last_reissued_at":"2026-05-18T03:51:01.899420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:01.899420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\phi_\\omega(x)e^{-i\\omega t}$. 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