A SYSTEMATIC METHOD OF FINDING LINEARIZING TRANSFORMATIONS FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS: II. EXTENSION TO COUPLED ODEs

作者：Chandrasekar V K^*; Senthilvelan M; Lakshmanan M

来源：Journal of Nonlinear Mathematical Physics, 2012, 19(2): 1250013.

DOI：10.1142/S1402925112500131

• Nonlinear ODEs
• linearization
• first integrals

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.

• 出版日期2012-6