{"paper":{"title":"Symmetries of a class of Nonlinear Third Order Partial Differential Equations","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"solv-int","authors_text":"Canterbury, E.L. Mansfield, P.A. Clarkson, T.J. Priestley (University of Kent, UK)","submitted_at":"1996-09-13T15:26:14Z","abstract_excerpt":"In this paper we study symmetry reductions of a class of nonlinear third order partial differential equations $u_t -\\epsilon u_{xxt} +2\\kappa u_x= u u_{xxx} +\\alpha u u_x +\\beta u_x u_{xx}$ where $\\epsilon$, $\\kappa$, $\\alpha$ and $\\beta$ are arbitrary constants. Three special cases of equation (1) have appeared in the literature, up to some rescalings. In each case the equation has admitted unusual travelling wave solutions: the Fornberg-Whitham equation, for the parameters $\\epsilon=1$, $\\alpha=-1$, $\\beta=3$ and $\\kappa=\\tfr12$, admits a wave of greatest height, as a peaked limiting form of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9609004","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"}