{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T04:41:46Z","timestamp":1775536906374,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> One of the authors recently introduced the concept of conjugate Hamiltonian systems: the solution of the equation h = H(p, q, t), where H is a given Hamiltonian containing t explicitly, yields the function t = T(p, q, h), which defines a new Hamiltonian system with Hamiltonian T and independent variable h. By employing this construction and by using the fact that the classical Painlev\u00e9 equations are Hamiltonian systems, it is straightforward to associate with each Painlev\u00e9 equation two new integrable ODEs. Here, we investigate the conjugate Painlev\u00e9 II equations. In particular, for these novel integrable ODEs, we present a Lax pair formulation, as well as a class of implicit solutions. We also construct conjugate equations associated with Painlev\u00e9 I and Painlev\u00e9 IV equations. <\/jats:p>","DOI":"10.1142\/s0218127412502112","type":"journal-article","created":{"date-parts":[[2012,10,16]],"date-time":"2012-10-16T02:49:37Z","timestamp":1350355777000},"page":"1250211","source":"Crossref","is-referenced-by-count":1,"title":["ON A NOVEL CLASS OF INTEGRABLE ODEs RELATED TO THE PAINLEV\u00c9 EQUATIONS"],"prefix":"10.1142","volume":"22","author":[{"given":"ATHANASSIOS S.","family":"FOKAS","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DI","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/0149071"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01197110"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1063\/1.525260"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01208781"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02099185"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/128"},{"key":"rf8","volume-title":"Ordinary Differential Equations (1926)","author":"Ince E. L.","year":"1956"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(81)90021-X"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/42\/5\/055208"},{"key":"rf11","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/223","volume-title":"Painlev\u00e9 Equations Through Symmetry","author":"Noumi M.","year":"2004"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(81)90026-9"},{"key":"rf13","first-page":"30","volume":"3","author":"Yablonskii A. I.","journal-title":"Vestsi Akad, Navuk BSSR Ser. Fiz.-Tech. Navuk"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412502112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:23:57Z","timestamp":1565187837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412502112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":12,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2012,10,15]]},"published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1142\/S0218127412502112"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412502112","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}