On the symmetry solutions of two-dimensional systems not solvable by standard symmetry analysis

Abstract

A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are linearizable, complex-linearizable and solvable systems. We also present the underlying concept diagrammatically that provides an analogue in ${\Re }^3$ of the geometric linearizability criteria in ${\Re }^2$.

This version is withdrawn because an updated version is uploaded by a co author on arXiv:1411.1182

References in corpus (3)

• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• Invariant Linearization Criteria for Systems of Cubically Semi-Linear Second-Order Ordinary Differential Equations
• A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: I. Scalar case

Cited by in corpus (2)

• Higher Dimensional Systems of Differential Equations Obtained by Iterative Use of Complex Methods
• Linearization of two dimensional complex-linearizable system of second order ordinary differential equations