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

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.

Accepted for publication in Proc. R. Soc. London A

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• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• On the complete integrability and linearization of nonlinear ordinary differential equations - Part II: Third order equations
• Explicit differential characterization of the Newtonian free particle system in m > 1 dependent variables
• Geometric Linearization of Ordinary Differential Equations
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• On the complete integrability and linearization of nonlinear ordinary differential equations - Part V: Linearization of coupled second order equations

Cited by in corpus (4)

• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• On the complete integrability of a nonlinear oscillator from group theoretical perspective
• On the complete integrability and linearization of nonlinear ordinary differential equations - Part V: Linearization of coupled second order equations
• Linearization from complex Lie point transformations