Exact analytic solutions of the Abel, Emden-Fowler and generalized Emden-Fowler nonlinear ODEs

Panayotounakos, DE; Kravvaritis, DC

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Kravvaritis, DC	en
dc.date.accessioned	2014-03-01T01:24:23Z
dc.date.available	2014-03-01T01:24:23Z
dc.date.issued	2006	en
dc.identifier.issn	1468-1218	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17235
dc.subject	Abel's equations	en
dc.subject	Emden-Fowler's equations	en
dc.subject	Exact analytic solutions	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Function evaluation	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Abel's equations	en
dc.subject.other	Emden-Fowler's equations	en
dc.subject.other	Exact analytic solutions	en
dc.subject.other	Nonlinear ODEs	en
dc.subject.other	Ordinary differential equations	en
dc.title	Exact analytic solutions of the Abel, Emden-Fowler and generalized Emden-Fowler nonlinear ODEs	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.nonrwa.2005.03.025	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.nonrwa.2005.03.025	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	Several basic particular nonlinear ordinary differential equations (ODEs) of the second-order in mathematical physics and nonlinear mechanics are reduced to equivalent equations of the Abel normal form yy(x)' - y = f (x) by means of various admissible functional transformations. These equivalent equations do not admit exact analytic solutions in terms of known (tabulated) functions, since only very special cases of the above type of Abel equation can be solved in parametric form [Kamke, Differentialgleichungen, Losungsmethoden und Losungen, vol. 1, B.G. Teubner, Stuttgard, 1977; Polyanin and Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, New York, 1999]. In this paper, a successful attempt is made to present a mathematical construction leading to the exact analytic solution of the above Abel equation. Since there are admissible functional transformations that reduce the Emden-Fowler equation y(xx)'',= Ax(n)y(m) and the generalized Emden-Fowler equation y(xx)" = Ax(n)y(m) (y(x)')(l) to the above Abel equation, the developed construction concerns also the analytic solutions of these two types of Emden-Fowler's nonlinear ODEs. (c) 2005 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Nonlinear Analysis: Real World Applications	en
dc.identifier.doi	10.1016/j.nonrwa.2005.03.025	en
dc.identifier.isi	ISI:000238823500011	en
dc.identifier.volume	7	en
dc.identifier.issue	4	en
dc.identifier.spage	634	en
dc.identifier.epage	650	en