{"paper":{"title":"Liouville integrability of conservative peakons for a modified CH equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Jacek Szmigielski, Xiang-Ke Chang","submitted_at":"2017-07-17T03:06:18Z","abstract_excerpt":"The modified Camassa-Holm equation (also called FORQ) is one of numerous $cousins$ of the Camassa-Holm equation possessing non-smoth solitons ($peakons$) as special solutions. The peakon sector of solutions is not uniquely defined: in one peakon sector (dissapative) the Sobolev $H^1$ norm is not preserved, in the other sector (conservative), introduced in [2], the time evolution of peakons leaves the $H^1$ norm invariant. In this Letter, it is shown that the conservative peakon equations of the modified Camassa-Holm can be given an appropriate Poisson structure relative to which the equations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04989","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"}