Linearizability Criteria for Systems of Two Second-Order Differential Equations by Complex Methods

Abstract

Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane-Emden type equations which have roots in the study of stellar structures are presented and discussed.

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