{"paper":{"title":"Modified Korteweg-de Vries equation: modulated elliptic wave and a train of asymptotic solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Minakov Alexander, Vladimir Kotlyarov","submitted_at":"2013-04-05T13:21:08Z","abstract_excerpt":"We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg - de Vries equation with an initial function of the step type. This function rapidly tends to zero as $x\\to+\\infty$ and to some positive constant c as $x\\to-\\infty$. In 1989 E. Khruslov and V. Kotlyarov have found that for a large time the solution breaks up into a train of asymptotic solitons located in the domain $4c^2t-C_N \\ln t<x\\leq4c^2t$ ($C_N$ is a constant). The number N of these solitons grows unboundedly as $t\\to\\infty$. In 2010 V. Kotlyarov and A. Minakov have studied temporary asymptotics of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1703","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":""},"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"}