On the complete integrability and linearization of nonlinear ordinary differential equations - Part V: Linearization of coupled second order equations

TL;DR

This paper presents a new, straightforward method for deriving linearizing transformations for coupled second order nonlinear ODEs, enabling their solutions and expanding the toolkit for solving complex differential systems.

Contribution

The paper introduces novel algorithms for linearizing coupled second order nonlinear ODEs, including both invertible and non-invertible transformations, with illustrative examples.

Findings

Derived new linearizing transformations for coupled SNODEs

Provided algorithms for obtaining general solutions

Demonstrated effectiveness with key examples

Abstract

Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to derive linearizing transformations for a class of two coupled SNODEs. Our procedure gives several new types of linearizing transformations of both invertible and non-invertible kinds. In both the cases we provide algorithms to derive the general solution of the given SNODE. We illustrate the theory with potentially important examples.