Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2012-01-26
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Accepted for Publication in J. Nonlinear Math. Phys. (2012)
Scientific paper
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.
Chandrasekar V. K.
Lakshmanan Meenakshi
Senthilvelan M.
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