Chandrasekar, V. K. ; Senthilvelan, M. ; Lakshmanan, M. (2009) On the complete integrability and linearization of nonlinear ordinary differential equations. III. Coupled first-order equations Proceedings of the Royal Society of London Series A: Mathematical, Physical & Engineering Sciences, 465 (2102). pp. 585-608. ISSN 0962-8444
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Official URL: http://rspa.royalsocietypublishing.org/content/465...
Related URL: http://dx.doi.org/10.1098/rspa.2008.0239
Abstract
Continuing our study on the complete integrability of nonlinear ordinary differential equations (ODEs), in this paper we consider the integrability of a system of coupled first-order nonlinear ODEs of both autonomous and non-autonomous types. For this purpose, we modify the original Prelle-Singer (PS) procedure so as to apply it to both autonomous and non-autonomous systems of coupled first-order ODEs. We briefly explain the method of finding integrals of motion (time-independent as well as time-dependent integrals) for two and three coupled first-order ODEs by extending the PS method. From this we try to answer some of the open questions in the original PS method. We also identify integrable cases for the two-dimensional Lotka-Volterra system and three-dimensional Rossler system as well as other examples including non-autonomous systems in a straightforward way using this procedure. Finally, we develop a linearization procedure for coupled first-order ODEs.
Item Type: | Article |
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Source: | Copyright of this article belongs to Royal Society Publishing. |
Keywords: | Nonlinear Differential Equations; Coupled first Order; Integrability; Integrating Factor; Linearization |
ID Code: | 19368 |
Deposited On: | 22 Nov 2010 12:43 |
Last Modified: | 17 May 2016 03:56 |
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