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When $b=2$ and $g$ is the peakon kernel (i.e. $g(x)=\\exp(-|x|)$ up to rescaling) the dispersionless Camassa-Holm equation results, while the Degasperis-Procesi equation is obtained from the peakon kernel with $b=3$. Although these two cases are integrable, generically the corresponding integro-PDE is non-integrable. However,for $b=2$ the family restricts to the pulson family of Fringer & Holm, which is Hamiltonian and numerically displays elastic scattering of pu"},"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":"nlin/0412029","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2004-12-10T17:44:59Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"9fe80c0165335c47e8a573cc3c30ecc04f440d51f1c3150d71eacb5e1c234811","abstract_canon_sha256":"e36fc0a254c7995856eae6593fcfe37029446e3d455ab825cdcd398194d6145c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:18.815732Z","signature_b64":"uoqGbTS0S3QF2+juCvFhaPcA8p1AMhWgN1joZ8m23ouqx3N6DKzvXWm10VJfQre4dYCkiq1rTsMEGHk2OSP1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77b87b221cb36476cd3377ff3ff5b114f8cc0e3e9058da9952562fe2cf6f87cc","last_reissued_at":"2026-05-18T01:38:18.815138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:18.815138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith)","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Andrew N.W. 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