{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HQDTOHHYMNYTLWPY22MWXJLNGD","short_pith_number":"pith:HQDTOHHY","schema_version":"1.0","canonical_sha256":"3c07371cf8637135d9f8d6996ba56d30ce57165b3db8053e0aad9e0f1c8c9b23","source":{"kind":"arxiv","id":"1412.7881","version":1},"attestation_state":"computed","paper":{"title":"On a two-component Bose-Einstein condensate with steep potential wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tsung-fang Wu, Wenming Zou, Yuanze Wu","submitted_at":"2014-12-26T02:20:23Z","abstract_excerpt":"In this paper, we study the following two-component systems of nonlinear Schr\\\"odinger equations \\begin{equation*} \\left\\{\\aligned&\\Delta u-(\\lambda a(x)+a_0(x))u+\\mu_1u^3+\\beta v^2u=0\\quad&\\text{in }\\bbr^3,\\\\ &\\Delta v-(\\lambda b(x)+b_0(x))v+\\mu_2v^3+\\beta u^2v=0\\quad&\\text{in }\\bbr^3,\\\\ &u,v\\in\\h,\\quad u,v>0\\quad\\text{in }\\bbr^3,\\endaligned\\right. \\end{equation*} where $\\lambda,\\mu_1,\\mu_2>0$ and $\\beta<0$ are parameters; $a(x), b(x)\\geq0$ are steep potentials and $a_0(x),b_0(x)$ are sign-changing weight functions; $a(x)$, $b(x)$, $a_0(x)$ and $b_0(x)$ are not necessarily to be radial symmet"},"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":"1412.7881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-26T02:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"eb862aa0c96f04411e16cf91c1cdd353680a44412acdbfa7333ac619d8667ec4","abstract_canon_sha256":"cd6139ad9d79700546d8c4c67ca8191a831f39002d4988b10675706dea88387f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:24.830251Z","signature_b64":"VQS19OgclpAT+AiJdppFO9oqHybSmg3cORWKMbXofRHLJcAomeG7uIQDIGshd1tnqnWyFrIiLjHvXJ0lvmHDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c07371cf8637135d9f8d6996ba56d30ce57165b3db8053e0aad9e0f1c8c9b23","last_reissued_at":"2026-05-18T02:30:24.829808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:24.829808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a two-component Bose-Einstein condensate with steep potential wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tsung-fang Wu, Wenming Zou, Yuanze Wu","submitted_at":"2014-12-26T02:20:23Z","abstract_excerpt":"In this paper, we study the following two-component systems of nonlinear Schr\\\"odinger equations \\begin{equation*} \\left\\{\\aligned&\\Delta u-(\\lambda a(x)+a_0(x))u+\\mu_1u^3+\\beta v^2u=0\\quad&\\text{in }\\bbr^3,\\\\ &\\Delta v-(\\lambda b(x)+b_0(x))v+\\mu_2v^3+\\beta u^2v=0\\quad&\\text{in }\\bbr^3,\\\\ &u,v\\in\\h,\\quad u,v>0\\quad\\text{in }\\bbr^3,\\endaligned\\right. \\end{equation*} where $\\lambda,\\mu_1,\\mu_2>0$ and $\\beta<0$ are parameters; $a(x), b(x)\\geq0$ are steep potentials and $a_0(x),b_0(x)$ are sign-changing weight functions; $a(x)$, $b(x)$, $a_0(x)$ and $b_0(x)$ are not necessarily to be radial symmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7881","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.7881","created_at":"2026-05-18T02:30:24.829859+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7881v1","created_at":"2026-05-18T02:30:24.829859+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7881","created_at":"2026-05-18T02:30:24.829859+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQDTOHHYMNYT","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQDTOHHYMNYTLWPY","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQDTOHHY","created_at":"2026-05-18T12:28:30.664211+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD","json":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD.json","graph_json":"https://pith.science/api/pith-number/HQDTOHHYMNYTLWPY22MWXJLNGD/graph.json","events_json":"https://pith.science/api/pith-number/HQDTOHHYMNYTLWPY22MWXJLNGD/events.json","paper":"https://pith.science/paper/HQDTOHHY"},"agent_actions":{"view_html":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD","download_json":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD.json","view_paper":"https://pith.science/paper/HQDTOHHY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7881&json=true","fetch_graph":"https://pith.science/api/pith-number/HQDTOHHYMNYTLWPY22MWXJLNGD/graph.json","fetch_events":"https://pith.science/api/pith-number/HQDTOHHYMNYTLWPY22MWXJLNGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD/action/storage_attestation","attest_author":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD/action/author_attestation","sign_citation":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD/action/citation_signature","submit_replication":"https://pith.science/pith/HQDTOHHYMNYTLWPY22MWXJLNGD/action/replication_record"}},"created_at":"2026-05-18T02:30:24.829859+00:00","updated_at":"2026-05-18T02:30:24.829859+00:00"}