A Systematic Method of Finding Linearizing Transformations for Nonlinear Ordinary Differential Equations II: Extension to Coupled ODEs

DOI

10.1142/S1402925112500131How to use a DOI?

Keywords

Nonlinear ODEs; linearization; first integrals

Abstract

In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second-order nonlinear ODEs. We show that beside the conventional point, Sundman and generalized linearizing transformations one can also find a large class of mixed or hybrid type linearizing transformations like point-Sundman, point-generalized linearizing transformation and Sundman-generalized linearizing transformation in coupled second-order ODEs using the integrals of motion. We propose suitable algorithms to identify all these transformations (with maximal in number) in a straightforward manner. We illustrate the method of deriving each one of the linearizing transformations with a suitable example.

Copyright

© 2012 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V. K. Chandrasekar
AU  - M. Senthilvelan
AU  - M. Lakshmanan
PY  - 2012
DA  - 2012/07/04
TI  - A Systematic Method of Finding Linearizing Transformations for Nonlinear Ordinary Differential Equations II: Extension to Coupled ODEs
JO  - Journal of Nonlinear Mathematical Physics
SP  - 203
EP  - 225
VL  - 19
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500131
DO  - 10.1142/S1402925112500131
ID  - Chandrasekar2012
ER  -