{"paper":{"title":"An analytic technique for the solutions of nonlinear oscillators with damping using the Abel Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A Ghose-Choudhury, Partha Guha","submitted_at":"2016-08-08T05:44:58Z","abstract_excerpt":"Using the Chiellini condition for integrability we derive explicit solutions for a generalized system of Riccati equations $\\ddot{x}+\\alpha x^{2n+1}\\dot{x}+x^{4n+3}=0$ by reduction to the first-order Abel equation assuming the parameter $\\alpha\\ge 2\\sqrt{2(n+1)}$. The technique, which was proposed by Harko \\textit{et al}, involves use of an auxiliary system of first-order differential equations sharing a common solution with the Abel equation. In the process analytical proofs of some of the conjectures made earlier on the basis of numerical investigations in \\cite{SJKB} is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02324","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"}