A systematic method of finding linearizing transformations for nonlinear   ordinary differential equations: II. Extension to coupled ODEs
  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. 
V. K. Chandrasekar, M. Senthilvelan and M. Lakshmanan
nlin.SI math-ph math.MP