{"paper":{"title":"Symmetries of a class of nonlinear fourth order partial differential equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peter A. Clarkson, Thomas J. Priestley","submitted_at":"1999-01-01T00:00:00Z","abstract_excerpt":"In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \\be u_{tt} = \\left(\\kappa u + \\gamma u^2\\right)_{xx} + u u_{xxxx} +\\mu u_{xxtt}+\\alpha u_x u_{xxx} + \\beta u_{xx}^2, \\ee where $\\alpha$, $\\beta$, $\\gamma$, $\\kappa$ and $\\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9901154","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"}