{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:04:00Z","timestamp":1753873440010,"version":"3.41.2"},"reference-count":14,"publisher":"AIP Publishing","issue":"6","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2014,6,1]]},"abstract":"<jats:p>We consider the general damped nonlinear oscillator x\u2032 = y, y\u2032 = \u2212a1x \u2212 a2xn+1 \u2212 a3x2n+1 \u2212 y(a4 + a5xn), where ai are real parameters for i = 1, 2, 3, 4, 5 and n is an integer. We note that these class of Li\u00e9nard differential systems include a large number of physically important nonlinear oscillators. We provide a complete and rigorous characterization of these systems that admit a local analytic first integral in a neighborhood of the origin.<\/jats:p>","DOI":"10.1063\/1.4882082","type":"journal-article","created":{"date-parts":[[2014,6,10]],"date-time":"2014-06-10T00:30:30Z","timestamp":1402360230000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["On the local analytic integrability for a generalized damped nonlinear oscillator equation"],"prefix":"10.1063","volume":"55","author":[{"given":"C.","family":"Valls","sequence":"first","affiliation":[{"name":"Universidade de Lisboa Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, , 1049-001 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2014,6,9]]},"reference":[{"key":"2023062722294569700_c1","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1063\/1.524491","article-title":"A connection between nonlinear evolution equations and ordinary differential equations of P-type I","volume":"21","year":"1980","journal-title":"J. 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