{"paper":{"title":"Solutions for one class of nonlinear fourth-order partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Supaporn Suksern","submitted_at":"2010-10-11T11:51:44Z","abstract_excerpt":"Some solutions for one class of nonlinear fourth-order partial differential equations \\[u_{tt} = ({\\kappa u + \\gamma u^2})_{xx} + \\nu uu_{xxxx} + \\mu u_{xxtt} + \\alpha u_x u_{xxx} + \\beta u_{xx}^2 \\] where $\\alpha ,\\;\\beta ,\\;\\gamma ,\\;\\mu ,\\,\\nu $ and $\\kappa $ are arbitrary constants are presented in the paper. 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. Furthermore, this equation is a Boussinesq-type equation which arises as a model of vibrations of harmonic mass-spring "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2075","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"}