{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DXVCEBU5XPEWAZJQHGVVQPLGZO","short_pith_number":"pith:DXVCEBU5","schema_version":"1.0","canonical_sha256":"1dea22069dbbc960653039ab583d66cba27f1b500fadc9daf7b609bec5c815eb","source":{"kind":"arxiv","id":"1810.04944","version":1},"attestation_state":"computed","paper":{"title":"Coupled Mode Equations and Gap Solitons in Higher Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Lisa Wahlers, Tomas Dohnal","submitted_at":"2018-10-11T10:34:05Z","abstract_excerpt":"We study waves-packets in nonlinear periodic media in arbitrary ($d$) spatial dimension, modeled by the cubic Gross-Pitaevskii equation. In the asymptotic setting of small and broad waves-packets with $N\\in \\mathbb{N}$ carrier Bloch waves the effective equations for the envelopes are first order coupled mode equations (CMEs). We provide a rigorous justification of the effective equations. The estimate of the asymptotic error is carried out in an $L^1$-norm in the Bloch variables. This translates to a supremum norm estimate in the physical variables. In order to investigate the existence of gap"},"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":"1810.04944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-11T10:34:05Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"title_canon_sha256":"95646ea56aba2180a37ce754a0044cea89e22cfaea38e77dd23f631d036d33e4","abstract_canon_sha256":"6f4b3cf287865da56355f408f61b37749d0a9a2f501f95053409b87f520e0132"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:35.436639Z","signature_b64":"f/ITPuJYpQarllFk/hR0D14Pu/5YyVlCSSd06Ra0HgR/Bge7CSgWdKhu3KZWLj2VUlQ14KiggZqn7b6ffc+dCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dea22069dbbc960653039ab583d66cba27f1b500fadc9daf7b609bec5c815eb","last_reissued_at":"2026-05-18T00:03:35.436128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:35.436128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupled Mode Equations and Gap Solitons in Higher Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Lisa Wahlers, Tomas Dohnal","submitted_at":"2018-10-11T10:34:05Z","abstract_excerpt":"We study waves-packets in nonlinear periodic media in arbitrary ($d$) spatial dimension, modeled by the cubic Gross-Pitaevskii equation. In the asymptotic setting of small and broad waves-packets with $N\\in \\mathbb{N}$ carrier Bloch waves the effective equations for the envelopes are first order coupled mode equations (CMEs). We provide a rigorous justification of the effective equations. The estimate of the asymptotic error is carried out in an $L^1$-norm in the Bloch variables. This translates to a supremum norm estimate in the physical variables. In order to investigate the existence of gap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04944","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":"1810.04944","created_at":"2026-05-18T00:03:35.436202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04944v1","created_at":"2026-05-18T00:03:35.436202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04944","created_at":"2026-05-18T00:03:35.436202+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXVCEBU5XPEW","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXVCEBU5XPEWAZJQ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXVCEBU5","created_at":"2026-05-18T12:32:19.392346+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/DXVCEBU5XPEWAZJQHGVVQPLGZO","json":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO.json","graph_json":"https://pith.science/api/pith-number/DXVCEBU5XPEWAZJQHGVVQPLGZO/graph.json","events_json":"https://pith.science/api/pith-number/DXVCEBU5XPEWAZJQHGVVQPLGZO/events.json","paper":"https://pith.science/paper/DXVCEBU5"},"agent_actions":{"view_html":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO","download_json":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO.json","view_paper":"https://pith.science/paper/DXVCEBU5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04944&json=true","fetch_graph":"https://pith.science/api/pith-number/DXVCEBU5XPEWAZJQHGVVQPLGZO/graph.json","fetch_events":"https://pith.science/api/pith-number/DXVCEBU5XPEWAZJQHGVVQPLGZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO/action/storage_attestation","attest_author":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO/action/author_attestation","sign_citation":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO/action/citation_signature","submit_replication":"https://pith.science/pith/DXVCEBU5XPEWAZJQHGVVQPLGZO/action/replication_record"}},"created_at":"2026-05-18T00:03:35.436202+00:00","updated_at":"2026-05-18T00:03:35.436202+00:00"}