On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations

Chandrasekar, V. K. ; Senthilvelan, M. ; Lakshmanan, M. (2009) On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations Proceedings of the Royal Society of London Series A: Mathematical, Physical & Engineering Sciences, 465 (2102). pp. 609-629. ISSN 0962-8444

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Official URL: http://rspa.royalsocietypublishing.org/content/465...

Related URL: http://dx.doi.org/10.1098/rspa.2008.0240

Abstract

Coupled second-order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations (ODEs), we focus our attention on the method of deriving a general solution for two coupled second-order nonlinear ODEs through the extended Prelle-Singer procedure. We describe a procedure to obtain integrating factors and the required number of integrals of motion so that the general solution follows straightforwardly from these integrals. Our method tackles both isotropic and non-isotropic cases in a systematic way. In addition to the above-mentioned method, we introduce a new method of transforming coupled second-order nonlinear ODEs into uncoupled ones. We illustrate the theory with potentially important examples.

Item Type:Article
Source:Copyright of this article belongs to Royal Society Publishing.
Keywords:Nonlinear Differential Equations; Coupled Second Order; Integrability; Integrating Factors; Uncoupling
ID Code:19365
Deposited On:22 Nov 2010 12:43
Last Modified:17 May 2016 03:55

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