Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - I: Ordinary Differential Equations

Abstract

The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of two real ordinary differential equations. The transformations that map a system of two nonlinear ordinary differential equations into systems of linear ordinary differential equations are obtained from complex transformations. Invariant criteria for linearization are given for second order complex ordinary differential equations in terms of the coefficients of the equations, as well as the corresponding real system, which provide procedures for writing down the solutions of the equations. Illustrative examples are given and discussed.

This paper along with its second part PDE-II were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics

References in corpus (3)

• Exact Analysis of the Adiabatic Invariants in Time-Dependent Harmonic Oscillator
• Constructing a Space from the System of Geodesic Equations
• Conditional linearizability criteria for a system of third-order ordinary differential equations

Cited by in corpus (4)

• Linearization from complex Lie point transformations
• Physical Significance of Noether Symmetries
• Linearization of Newton's second law
• $\lambda$-symmetry criteria for linearization of second order ODEs via point transformations