{"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. Hone, Darryl D. Holm","submitted_at":"2004-12-10T17:44:59Z","abstract_excerpt":"We consider a family of integro-differential equations depending upon a parameter $b$ as well as a symmetric integral kernel $g(x)$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0412029","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"}