{"paper":{"title":"Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev--Petviashvili equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mark Groves, Mats Ehrnstr\\\"om","submitted_at":"2018-02-13T19:10:33Z","abstract_excerpt":"The KP-I equation \\[ (u_t-2uu_x+\\tfrac{1}{2}(\\beta-\\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \\] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\\beta>1/3$). This equation admits --- as an explicit solution --- a `fully localised' or `lump' solitary wave which decays to zero in all spatial directions. Recently there has been interest in the \\emph{full-dispersion KP-I equation} \\[u_t + m({\\mathrm D}) u_x + 2 u u_x = 0,\\] where $m({\\mathrm D})$ is the Fourier multiplier with symbol \\[ m(k) = \\left( 1 + \\beta |k|^2|\\right)^{\\frac{1}{2}} \\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04823","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"}