{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EHFVDQJFZHDANM7WPASDOJ6E72","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a4f20a6a1cc3a708ed90a63816aa77e3172ad4d819a4f097adbd04a82656cb11","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-12-19T22:47:34Z","title_canon_sha256":"90bd60e27c671dac0a7a3e2854933adbb765b74bd0886ef48eab699618f6e00b"},"schema_version":"1.0","source":{"id":"1301.3474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3474","created_at":"2026-05-18T01:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3474v1","created_at":"2026-05-18T01:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3474","created_at":"2026-05-18T01:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"EHFVDQJFZHDA","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EHFVDQJFZHDANM7W","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EHFVDQJF","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:8a318842836078a2f9930f8384c299c53f32ef7a814dae82034cbdb849a1c8c6","target":"graph","created_at":"2026-05-18T01:31:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate periodic and solitary wave solutions of the modified Benjamin, Bona & Mahony equation (BBM) to include both dissipative and dispersive effects of viscous boundary layers. Under certain circumstances that depend on the traveling wave velocity, classes of periodic and solitary wave like solutions are obtained in terms of Jacobi elliptic functions. An ad-hoc theory based on the dissipative term is presented, in which we have found a set of solutions in terms of an implicit function","authors_text":"Harihar Khanal, Shardad G. Sajjadi, Stefan C. Mancas","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-12-19T22:47:34Z","title":"Solitary waves, periodic and elliptic solutions to the Benjamin, Bona & Mahony (BBM) equation modified by viscosity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3474","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:da5aa541a9b1f7c9d6698d9656f3e981b9e5f960786d78870e02c1c180f6ac08","target":"record","created_at":"2026-05-18T01:31:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a4f20a6a1cc3a708ed90a63816aa77e3172ad4d819a4f097adbd04a82656cb11","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2012-12-19T22:47:34Z","title_canon_sha256":"90bd60e27c671dac0a7a3e2854933adbb765b74bd0886ef48eab699618f6e00b"},"schema_version":"1.0","source":{"id":"1301.3474","kind":"arxiv","version":1}},"canonical_sha256":"21cb51c125c9c606b3f678243727c4fe89ad773c66fd8b964ab5bddbf5edb8ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21cb51c125c9c606b3f678243727c4fe89ad773c66fd8b964ab5bddbf5edb8ef","first_computed_at":"2026-05-18T01:31:30.485029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:30.485029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pmt/2uVEowC3Uai1TpmDw2YC6cTGPb+LQqvZsLv89sIe3wAKOJ5RvWT0VVE1OBqEb87RdfJ6PVhKNuzGOPpdCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:30.485620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da5aa541a9b1f7c9d6698d9656f3e981b9e5f960786d78870e02c1c180f6ac08","sha256:8a318842836078a2f9930f8384c299c53f32ef7a814dae82034cbdb849a1c8c6"],"state_sha256":"070fcd7a2c79295824ab58c76a9ac8b16934d600079363b63a2afb5066c8bf03"}