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

TL;DR

This paper extends a method for finding linearizing transformations to coupled second order nonlinear ODEs, introducing hybrid transformations and algorithms to identify all such transformations systematically.

Contribution

It introduces a systematic approach to derive various linearizing transformations, including hybrid types, for coupled nonlinear ODEs, expanding the scope of previous methods.

Findings

Identified a large class of hybrid linearizing transformations

Developed algorithms to find all transformations systematically

Demonstrated the method with illustrative examples

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.