{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3HDCTMXSBNIDXHBSEKO6S3OIH6","short_pith_number":"pith:3HDCTMXS","schema_version":"1.0","canonical_sha256":"d9c629b2f20b503b9c32229de96dc83f83a4a445453a8895a41c4f96140bab86","source":{"kind":"arxiv","id":"1407.5371","version":4},"attestation_state":"computed","paper":{"title":"Analysis on an extended Majda--Biello system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Yezheng Li","submitted_at":"2014-07-21T04:35:00Z","abstract_excerpt":"In this paper, we begin with extended Majda--Biello system (BSAB equations): $$ \\left\\{\\begin{array}{l} 0=A_t-DA_3+\\mu A_1+\\Gamma_S B^S_1+\\Gamma_A B_1^A+\\left(AB^S\\right)_x \\\\ 0=B^S_t-B_3^S+\\Gamma_SA_1+\\lambda B_1^S+\\sigma B^A_1+AA_1 \\\\ 0=B^A_t-B_3^A+\\Gamma_A A_1+\\sigma B_1^S-\\lambda B_1^A \\end{array}\\right. $$\n  We conclude global well-posedness in $L^2(\\mathbb{R})\\times L^2(\\mathbb{R})\\times L^2(\\mathbb{R})$ by Brougain's method and the stability of solitary wave solutions by putting it in a framework of generalised KdV type system with three components, where Hamiltonian structure plays an "},"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":"1407.5371","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T04:35:00Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"ca4adb8e16f169adb2a1dab0bf0f19cae20975c39dce57eef2df033046b525c5","abstract_canon_sha256":"63c2564c33a8b10e55f3c57b065c37216264a09a14bc32ecbc91a0b9f415d8c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:10.831144Z","signature_b64":"8uYdsIROMLzSAaDW9ZCgJVnH1yJIHKQiGoku5YzwyJTN7F2I5sZMTQw7Ch8IsGds0qHLiy36Pt6SZqdqPG1ACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c629b2f20b503b9c32229de96dc83f83a4a445453a8895a41c4f96140bab86","last_reissued_at":"2026-05-18T02:29:10.830566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:10.830566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis on an extended Majda--Biello system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Yezheng Li","submitted_at":"2014-07-21T04:35:00Z","abstract_excerpt":"In this paper, we begin with extended Majda--Biello system (BSAB equations): $$ \\left\\{\\begin{array}{l} 0=A_t-DA_3+\\mu A_1+\\Gamma_S B^S_1+\\Gamma_A B_1^A+\\left(AB^S\\right)_x \\\\ 0=B^S_t-B_3^S+\\Gamma_SA_1+\\lambda B_1^S+\\sigma B^A_1+AA_1 \\\\ 0=B^A_t-B_3^A+\\Gamma_A A_1+\\sigma B_1^S-\\lambda B_1^A \\end{array}\\right. $$\n  We conclude global well-posedness in $L^2(\\mathbb{R})\\times L^2(\\mathbb{R})\\times L^2(\\mathbb{R})$ by Brougain's method and the stability of solitary wave solutions by putting it in a framework of generalised KdV type system with three components, where Hamiltonian structure plays an 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