{"paper":{"title":"A Simple and Unified Approach to Identify Integrable Nonlinear Oscillators and Systems","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"M. Lakshmanan, M. Senthilvelan, S. N. Pandey, V. K. Chandrasekar","submitted_at":"2005-11-15T11:40:55Z","abstract_excerpt":"In this paper, we consider a generalized second order nonlinear ordinary differential equation of the form $\\ddot{x}+(k_1x^q+k_2)\\dot{x}+k_3x^{2q+1}+k_4x^{q+1}+\\lambda_1x=0$, where $k_i$'s, $i=1,2,3,4$, $\\lambda_1$ and $q$ are arbitrary parameters, which includes several physically important nonlinear oscillators such as the simple harmonic oscillator, anharmonic oscillator, force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden type equation and its hierarchy, generalized Duffing-van der Pol oscillator equation hierarchy and so on and investiga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0511030","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"}