On the reduction and the existence of approximate analytic solutions of some basic nonlinear ODEs in mathematical physics and nonlinear mechanics

Panayotounakos, DE; Sotiropoulos, NV

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Sotiropoulos, NV	en
dc.date.accessioned	2014-03-01T01:21:10Z
dc.date.available	2014-03-01T01:21:10Z
dc.date.issued	2004	en
dc.identifier.issn	0022-2488	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16115
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	OSCILLATOR	en
dc.subject.other	WAVES	en
dc.title	On the reduction and the existence of approximate analytic solutions of some basic nonlinear ODEs in mathematical physics and nonlinear mechanics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1063/1.1635065	en
heal.identifier.secondary	http://dx.doi.org/10.1063/1.1635065	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	Using series of admissible functional transformations we reduce the one-dimensional axisymmetric nonlinear Schrodinger (NLS) equation, as well as the forced damped nonlinear Duffing (NLD) equation to equivalent nonlinear first-order integrodifferential equations. The forced undamped (NLD) equation results as a special case. The reduced integrodifferential equations are exact. In the limits of small or large values of the parameters characterizing these nonlinear problems, we prove that further reductions lead to first-order nonlinear ordinary differential equations which, except in case of the (NLS) equation, are of the Abel classes. The approximate reduced (NLS) equation admits exact analytic solutions. On the other hand, taking into account the known exact analytic solutions of the equivalent Abel classes of equations we show that there do not exist analytic solutions of the above two nonlinear Duffing oscillators. However, if further asymptotic approximations take place, new approximate analytic solutions concerning the (NLD) equations are constructed. (C) 2004 American Institute of Physics.	en
heal.publisher	AMER INST PHYSICS	en
heal.journalName	Journal of Mathematical Physics	en
dc.identifier.doi	10.1063/1.1635065	en
dc.identifier.isi	ISI:000188281900019	en
dc.identifier.volume	45	en
dc.identifier.issue	2	en
dc.identifier.spage	803	en
dc.identifier.epage	826	en