{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:URBCXTJ42TT4ZTBXEFNJ667LZA","short_pith_number":"pith:URBCXTJ4","schema_version":"1.0","canonical_sha256":"a4422bcd3cd4e7cccc37215a9f7bebc827440e24be6113a14a5dc3e1b76a3b22","source":{"kind":"arxiv","id":"1512.00441","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic stability in the energy space for dark solitons of the Landau-Lifshitz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yakine Bahri","submitted_at":"2015-12-01T20:52:24Z","abstract_excerpt":"We prove the asymptotic stability in the energy space of non-zero speed solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy. More precisely, we show that any solution corresponding to an initial datum close to a soliton with non-zero speed, is weakly convergent in the energy space as time goes to infinity, to a soliton with a possible different non-zero speed, up to the invariances of the equation. Our analysis relies on the ideas developed by Martel and Merle for the generalized Korteweg-de Vries equations. We use the Madelung transform to study the problem"},"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":"1512.00441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-01T20:52:24Z","cross_cats_sorted":[],"title_canon_sha256":"385ac81054b3436e5a9c8fbfbf10c9bba41d722aafb1acdc97d9ff623c27f1aa","abstract_canon_sha256":"4873b9884a92235798e740ae456f6779139557075275c7c09bdcee3b9f28beef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:31.975355Z","signature_b64":"FM0FWAV+c+y7yvFOpHZSI/3nuAVcrHgE8yAZclZUR9Jhsrrx98gq5mfLx2rA7Ho84+PrK8eQZZzCsolZ44V1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4422bcd3cd4e7cccc37215a9f7bebc827440e24be6113a14a5dc3e1b76a3b22","last_reissued_at":"2026-05-18T01:11:31.974777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:31.974777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic stability in the energy space for dark solitons of the Landau-Lifshitz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yakine Bahri","submitted_at":"2015-12-01T20:52:24Z","abstract_excerpt":"We prove the asymptotic stability in the energy space of non-zero speed solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy. More precisely, we show that any solution corresponding to an initial datum close to a soliton with non-zero speed, is weakly convergent in the energy space as time goes to infinity, to a soliton with a possible different non-zero speed, up to the invariances of the equation. Our analysis relies on the ideas developed by Martel and Merle for the generalized Korteweg-de Vries equations. We use the Madelung transform to study the problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00441","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":"1512.00441","created_at":"2026-05-18T01:11:31.974862+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00441v1","created_at":"2026-05-18T01:11:31.974862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00441","created_at":"2026-05-18T01:11:31.974862+00:00"},{"alias_kind":"pith_short_12","alias_value":"URBCXTJ42TT4","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"URBCXTJ42TT4ZTBX","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"URBCXTJ4","created_at":"2026-05-18T12:29:44.643036+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/URBCXTJ42TT4ZTBXEFNJ667LZA","json":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA.json","graph_json":"https://pith.science/api/pith-number/URBCXTJ42TT4ZTBXEFNJ667LZA/graph.json","events_json":"https://pith.science/api/pith-number/URBCXTJ42TT4ZTBXEFNJ667LZA/events.json","paper":"https://pith.science/paper/URBCXTJ4"},"agent_actions":{"view_html":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA","download_json":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA.json","view_paper":"https://pith.science/paper/URBCXTJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00441&json=true","fetch_graph":"https://pith.science/api/pith-number/URBCXTJ42TT4ZTBXEFNJ667LZA/graph.json","fetch_events":"https://pith.science/api/pith-number/URBCXTJ42TT4ZTBXEFNJ667LZA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA/action/storage_attestation","attest_author":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA/action/author_attestation","sign_citation":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA/action/citation_signature","submit_replication":"https://pith.science/pith/URBCXTJ42TT4ZTBXEFNJ667LZA/action/replication_record"}},"created_at":"2026-05-18T01:11:31.974862+00:00","updated_at":"2026-05-18T01:11:31.974862+00:00"}