{"paper":{"title":"Stability of the train of $N$ solitary waves for the two-component Camassa-Holm shallow water system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xingxing Liu","submitted_at":"2015-09-27T02:41:24Z","abstract_excerpt":"Considered herein is the integrable two-component Camassa-Holm shallow water system derived in the context of shallow water theory, which admits blow-up solutions and the solitary waves interacting like solitons. Using modulation theory, and combining the almost monotonicity of a local version of energy with the argument on the stability of a single solitary wave, we prove that the train of $N$ solitary waves, which are sufficiently decoupled, is orbitally stable in the energy space $H^1(\\R)\\times L^2(\\R)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08044","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"}