A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: II. Extension to coupled ODEs

V. K. Chandrasekar; M. Senthilvelan; M. Lakshmanan

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arXiv · 1201.5445

A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: II. Extension to coupled ODEs

V. K. Chandrasekar·M. Senthilvelan·M. Lakshmanan

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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 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.

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BibTeX RIS

V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan. 2012-01-26. A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: II. Extension to coupled ODEs. https://arxiv.org/abs/1201.5445

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