{"paper":{"title":"Orbital Stability of Periodic Waves for the Log-KdV Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ademir Pastor, F\\'abio Natali, Fabr\\'icio Crist\\'ofani","submitted_at":"2014-08-07T20:48:24Z","abstract_excerpt":"In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \\cite{carles}, in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in \\cite{natali1} to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in \\cite{grillakis1} and \\cite{weinstein1} to deduce the orbital stability of the periodic t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1709","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"}