{"paper":{"title":"Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Anne De Bouard (CMAP), Eric Gautier (CREST)","submitted_at":"2008-01-25T08:08:18Z","abstract_excerpt":"We consider two exit problems for the Korteweg-de Vries equation perturbed by an additive white in time and colored in space noise of amplitude a. The initial datum gives rise to a soliton when a=0. It has been proved recently that the solution remains in a neighborhood of a randomly modulated soliton for times at least of the order of a^{-2}. We prove exponential upper and lower bounds for the small noise limit of the probability that the exit time from a neighborhood of this randomly modulated soliton is less than T, of the same order in a and T. We obtain that the time scale is exactly the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3894","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"}