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We establish, in particular, the existence of travelling waves with speed arbitrary large if $p<0$ and arbitrary close to $0$ if $p>\\frac 23$. We also show the existence of standing waves in the case $-1<p\\leq \\frac 23$, with compact support if $-1<p<0$.\\\\ Finally, we obtain, under certain conditions, the linearized stability of such solutions."},"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":"1403.0199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-02T11:58:18Z","cross_cats_sorted":[],"title_canon_sha256":"dfe4700dfa85cb6ac9672cbad6becc732fb7b5093dda4f10da334d0f56133fab","abstract_canon_sha256":"100892e6c9f41550bbd72acfa302df3f14aad6b593c5380d3aa443f5e690d6c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:25.493617Z","signature_b64":"KS+VushejXicnaK2i70mioCm8FftxxuGMe+2GCgKYLRrcq4u+IdZb/c2CWqGRPxyN2yT9CZUjXNShJg8FdJAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"746f4bd0d10a1c794039a0830c9b3ace52e1c68cb795c255394ef05fa1203e85","last_reissued_at":"2026-05-18T02:57:25.493059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:25.493059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and linearized stability of solitary waves for a quasilinear Benney system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira, Jo\\~ao-Paulo Dias, M\\'ario Figueira","submitted_at":"2014-03-02T11:58:18Z","abstract_excerpt":"We prove the existence of solitary wave solutions to the quasilinear Benney system $$iu_{t}+u_{xx}=a|u|^pu+uv,\\quad v_t+f(v)_x=(|u|^2)_x$$ where $f(v)=-\\gamma v^3$, $-1<p<+\\infty$ and $a,\\gamma>0$. We establish, in particular, the existence of travelling waves with speed arbitrary large if $p<0$ and arbitrary close to $0$ if $p>\\frac 23$. We also show the existence of standing waves in the case $-1<p\\leq \\frac 23$, with compact support if $-1<p<0$.\\\\ Finally, we obtain, under certain conditions, the linearized stability of such solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0199","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":"1403.0199","created_at":"2026-05-18T02:57:25.493139+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.0199v1","created_at":"2026-05-18T02:57:25.493139+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0199","created_at":"2026-05-18T02:57:25.493139+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORXUXUGRBIOH","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORXUXUGRBIOHSQBZ","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORXUXUGR","created_at":"2026-05-18T12:28:43.426989+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/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ","json":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ.json","graph_json":"https://pith.science/api/pith-number/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/graph.json","events_json":"https://pith.science/api/pith-number/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/events.json","paper":"https://pith.science/paper/ORXUXUGR"},"agent_actions":{"view_html":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ","download_json":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ.json","view_paper":"https://pith.science/paper/ORXUXUGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.0199&json=true","fetch_graph":"https://pith.science/api/pith-number/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/action/storage_attestation","attest_author":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/action/author_attestation","sign_citation":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/action/citation_signature","submit_replication":"https://pith.science/pith/ORXUXUGRBIOHSQBZUCBQZGZ2ZZ/action/replication_record"}},"created_at":"2026-05-18T02:57:25.493139+00:00","updated_at":"2026-05-18T02:57:25.493139+00:00"}