{"paper":{"title":"$L^2$-stability of solitary waves for the KdV equation via Pego and Weinstein's method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikolay Tzvetkov, Tetsu Mizumachi","submitted_at":"2014-03-20T23:12:26Z","abstract_excerpt":"In this article, we will prove $L^2(\\mathbb{R})$-stability of $1$-solitons for the KdV equation by using exponential stability property of the semigroup generated by the linearized operator. The proof follows the lines of recent stability argument of Mizumachi [Asymptotic stability of lattice solitons in the energy space, Comm. Math. Phys., (2009)] and Mizumachi, Pego and Quintero [Asymptotic stability of solitary waves in the Benney-Luke model of water waves, Differential Integral Equations, (2013)] which show stability in the energy class by using strong linear stability of solitary waves in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5321","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"}