{"paper":{"title":"Stability and Decay properties of Solitary wave solutions for the generalized BO-ZK equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ademir Pastor, Amin Esfahani, Jerry L. Bona","submitted_at":"2009-09-10T19:31:57Z","abstract_excerpt":"Studied here is the generalized Benjamin-Ono--Zakharov-Kuznetsov equation $u_t+u^pu_x+\\alpha\\mathscr{H}u_{xx}+\\varepsilon u_{xyy}=0, \\quad (x,y)\\in\\rr^2\\!,\\;\\;t\\in \\rr^+\\!$ in two space dimensions. Here, $\\mathscr{H}$ is the Hilbert transform and subscripts denote partial differentiation. We classify when equation (1) possesses solitary-wave solutions in terms of the signs of the constants $\\alpha$ and $\\varepsilon$ appearing in the dispersive terms and the strength of the nonlinearity. Regularity and decay properties of these solitary wave are determined and their stability is studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2020","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"}