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 besides 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.
@article{arxiv.1201.5445,
title = {A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: II. Extension to coupled ODEs},
author = {V. K. Chandrasekar and M. Senthilvelan and M. Lakshmanan},
journal= {arXiv preprint arXiv:1201.5445},
year = {2012}
}
Comments
Accepted for Publication in J. Nonlinear Math. Phys. (2012)