Linearisable third order ordinary differential equations and generalised Sundman transformations

Abstract

We calculate in detail the conditions which allow the most general third order ordinary differential equation to be linearised in X'''(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are considered.

33 pages

References in corpus (3)

• The harmony in the Kepler and related problems
• Symmetry, singularities and integrability in complex dynamics I: the reduction problem
• A tree of linearisable second-order evolution equations by generalised hodograph transformations

Cited by in corpus (5)

• Linearization of Second-Order Ordinary Differential Equations by Generalized Sundman Transformations
• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
• Symmetry, Equivalence and Integrable Classes of Abel Equations
• Integrability cases for the anharmonic oscillator equation