{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5EYMWBGQVBOJNSCDSUVJ6NNZXQ","short_pith_number":"pith:5EYMWBGQ","schema_version":"1.0","canonical_sha256":"e930cb04d0a85c96c843952a9f35b9bc167bfbbc623903861a32d5d36a0a9b6e","source":{"kind":"arxiv","id":"1412.0306","version":2},"attestation_state":"computed","paper":{"title":"The nonlinear Schr\\\"odinger equation with $t$-periodic data: II. Perturbative results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AP","authors_text":"A. S. Fokas, J. Lenells","submitted_at":"2014-11-30T23:29:56Z","abstract_excerpt":"We consider the nonlinear Schr\\\"odinger equation on the half-line with a given Dirichlet boundary datum which for large $t$ tends to a periodic function. We assume that this function is sufficiently small, namely that it can be expressed in the form $\\alpha g_0^b(t)$, where $\\alpha$ is a small constant. Assuming that the Neumann boundary value tends for large $t$ to the periodic function $g_1^b(t)$, we show that $g_1^b(t)$ can be expressed in terms of a perturbation series in $\\alpha$ which can be constructed explicitly to any desired order. As an illustration, we compute $g_1^b(t)$ to order $"},"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":"1412.0306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-30T23:29:56Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"f8ca36d27474cb92e1c81dd18c7e56fddfa75ccf1268770a224be4a9b8c9ea9d","abstract_canon_sha256":"d381c587a7cf84c6cc1fa15320b55bbd1d4dddffdbc158d7c9224ad106da70b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:47.277517Z","signature_b64":"jyLqFA6mJRJa49FCdfyvZc85KpDpuBRLjbu6b0sS+yiaL2Gsoi0Czzk6R3XLWsM5X7hCBCsq1ty8m7QUgk3GAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e930cb04d0a85c96c843952a9f35b9bc167bfbbc623903861a32d5d36a0a9b6e","last_reissued_at":"2026-05-18T01:20:47.276956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:47.276956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The nonlinear Schr\\\"odinger equation with $t$-periodic data: II. Perturbative results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AP","authors_text":"A. S. Fokas, J. Lenells","submitted_at":"2014-11-30T23:29:56Z","abstract_excerpt":"We consider the nonlinear Schr\\\"odinger equation on the half-line with a given Dirichlet boundary datum which for large $t$ tends to a periodic function. We assume that this function is sufficiently small, namely that it can be expressed in the form $\\alpha g_0^b(t)$, where $\\alpha$ is a small constant. Assuming that the Neumann boundary value tends for large $t$ to the periodic function $g_1^b(t)$, we show that $g_1^b(t)$ can be expressed in terms of a perturbation series in $\\alpha$ which can be constructed explicitly to any desired order. As an illustration, we compute $g_1^b(t)$ to order $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0306","kind":"arxiv","version":2},"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":"1412.0306","created_at":"2026-05-18T01:20:47.277051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0306v2","created_at":"2026-05-18T01:20:47.277051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0306","created_at":"2026-05-18T01:20:47.277051+00:00"},{"alias_kind":"pith_short_12","alias_value":"5EYMWBGQVBOJ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5EYMWBGQVBOJNSCD","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5EYMWBGQ","created_at":"2026-05-18T12:28:14.216126+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/5EYMWBGQVBOJNSCDSUVJ6NNZXQ","json":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ.json","graph_json":"https://pith.science/api/pith-number/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/graph.json","events_json":"https://pith.science/api/pith-number/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/events.json","paper":"https://pith.science/paper/5EYMWBGQ"},"agent_actions":{"view_html":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ","download_json":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ.json","view_paper":"https://pith.science/paper/5EYMWBGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0306&json=true","fetch_graph":"https://pith.science/api/pith-number/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/graph.json","fetch_events":"https://pith.science/api/pith-number/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/action/storage_attestation","attest_author":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/action/author_attestation","sign_citation":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/action/citation_signature","submit_replication":"https://pith.science/pith/5EYMWBGQVBOJNSCDSUVJ6NNZXQ/action/replication_record"}},"created_at":"2026-05-18T01:20:47.277051+00:00","updated_at":"2026-05-18T01:20:47.277051+00:00"}