On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations

Chandrasekar, V. K. ; Senthilvelan, M. ; Lakshmanan, M. (2006) On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations Proceedings of the Royal Society of London Series A: Mathematical, Physical & Engineering Sciences, 462 (2070). pp. 1831-1852. ISSN 0962-8444

[img]
Preview
PDF - Publisher Version
319kB

Official URL: http://rspa.royalsocietypublishing.org/content/462...

Related URL: http://dx.doi.org/10.1098/rspa.2005.1648

Abstract

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals of motion associated with the given equation, so that the general solution follows straightforwardly from these integrals. The method is illustrated with several examples. Further, we propose a powerful method of identifying linearizing transformations. The proposed method not only unifies all the known linearizing transformations systematically but also introduces a new and generalized linearizing transformation. In addition to the above, we provide an algorithm to invert the non-local linearizing transformation. Through this procedure the general solution for the original nonlinear equation can be obtained from the solution of the linear ordinary differential equation.

Item Type:Article
Source:Copyright of this article belongs to Royal Society Publishing.
Keywords:Integrability; Integrating Factor; Linearization; Equivalence Problem
ID Code:19377
Deposited On:22 Nov 2010 12:42
Last Modified:17 May 2016 03:56

Repository Staff Only: item control page