{"paper":{"title":"Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongxiao Yu, Herbert Koch","submitted_at":"2023-08-15T10:12:14Z","abstract_excerpt":"We study the asymptotic stability of the sine-Gordon kinks under small perturbations in weighted Sobolev norms. Our main tool is the B\\\"acklund transform which reduces the study of the asymptotic stability of the kinks to the study of the asymptotic decay of solutions near zero. Our results consist of two parts. First, we prove an asymptotic stability result similar to the local results in arXiv:2003.09358 and arXiv:2009.04260. Our assumptions are the same as those in the local result in arXiv:2009.04260. In its proof, we apply a result obtained by the inverse scattering method on the local de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07679","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.07679/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}