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Under some assumptions on $f$, this equation admits \\emph{solitary waves}, that is solutions of the form $u(t, x) = Q_v(x - vt - x_0)$, for $v$ in some range $(0, v_*)$. We study pure two-solitons in the case of the same limit speed, in other words global solutions $u(t)$ such that \\begin{equation} \\label{eq:abstract} \\tag{$\\ast$} \\lim_{t\\to\\infty}\\|u(t) - (Q_v(\\cdot - x_1(t)) \\pm Q_v(\\cdot - x_2(t)))\\|_{H^1} = 0, \\qquad \\text{with}\\quad\\li"},"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":"1802.06294","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-17T21:13:40Z","cross_cats_sorted":[],"title_canon_sha256":"9725b956b047b65145352b97b89d70ef196f4be25e3ac2293536c9a0ecfa831d","abstract_canon_sha256":"a01b7908089cc622567e7d90525c7b9a343bf7ffeaf0ec507834b3d0a420d541"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:59:11.911091Z","signature_b64":"x4pEmy6kXX4+8h61mamGG4GPdWRmR233gqZT00roI57EYrnP8dNaUY2kkpK0k5S21jEoyJPcO+s9/Wbzp9X4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0e6342d691cf00a51e1f18dde3800869deba8599993e70518e24a64db0a9cf8","last_reissued_at":"2026-07-05T07:59:11.910614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:59:11.910614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of strongly interacting unstable two-solitons for generalized Korteweg-de Vries equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacek Jendrej","submitted_at":"2018-02-17T21:13:40Z","abstract_excerpt":"We consider the generalized Korteweg-de Vries equation $\\partial_t u = -\\partial_x(\\partial_x^2 u + f(u))$, where $f(u)$ is an odd function of class $C^3$. Under some assumptions on $f$, this equation admits \\emph{solitary waves}, that is solutions of the form $u(t, x) = Q_v(x - vt - x_0)$, for $v$ in some range $(0, v_*)$. We study pure two-solitons in the case of the same limit speed, in other words global solutions $u(t)$ such that \\begin{equation} \\label{eq:abstract} \\tag{$\\ast$} \\lim_{t\\to\\infty}\\|u(t) - (Q_v(\\cdot - x_1(t)) \\pm Q_v(\\cdot - x_2(t)))\\|_{H^1} = 0, \\qquad \\text{with}\\quad\\li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06294","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1802.06294/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1802.06294","created_at":"2026-07-05T07:59:11.910673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06294v2","created_at":"2026-07-05T07:59:11.910673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06294","created_at":"2026-07-05T07:59:11.910673+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDTDILLJDTYA","created_at":"2026-07-05T07:59:11.910673+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDTDILLJDTYAUUPB","created_at":"2026-07-05T07:59:11.910673+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDTDILLJ","created_at":"2026-07-05T07:59:11.910673+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.16274","citing_title":"Classification of kink clusters for scalar fields in dimension 1+1","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2","json":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2.json","graph_json":"https://pith.science/api/pith-number/UDTDILLJDTYAUUPB6GG54OAAQ2/graph.json","events_json":"https://pith.science/api/pith-number/UDTDILLJDTYAUUPB6GG54OAAQ2/events.json","paper":"https://pith.science/paper/UDTDILLJ"},"agent_actions":{"view_html":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2","download_json":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2.json","view_paper":"https://pith.science/paper/UDTDILLJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06294&json=true","fetch_graph":"https://pith.science/api/pith-number/UDTDILLJDTYAUUPB6GG54OAAQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/UDTDILLJDTYAUUPB6GG54OAAQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2/action/storage_attestation","attest_author":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2/action/author_attestation","sign_citation":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2/action/citation_signature","submit_replication":"https://pith.science/pith/UDTDILLJDTYAUUPB6GG54OAAQ2/action/replication_record"}},"created_at":"2026-07-05T07:59:11.910673+00:00","updated_at":"2026-07-05T07:59:11.910673+00:00"}