{"paper":{"title":"Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AP","authors_text":"Claudio Mu\\~noz, Miguel Angel Alejo","submitted_at":"2013-08-05T14:52:07Z","abstract_excerpt":"We study the long-time dynamics of complex-valued modified Korteweg-de Vries (mKdV) solitons, which are recognized because they blow-up in finite time. We establish stability properties at the H^1 level of regularity, uniformly away from each blow-up point. These new properties are used to prove that mKdV breathers are H^1 stable, improving our previous result, where we only proved H^2 stability. The main new ingredient of the proof is the use of a B\\\"acklund transformation which links the behavior of breathers, complex-valued solitons and small real-valued solutions of the mKdV equation. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0998","kind":"arxiv","version":3},"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"}