Linearizability Criteria for Systems of Two Second-Order Differential Equations by Complex Methods
Classical Analysis and ODEs
2011-07-25 v3
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.
Cite
@article{arxiv.1001.4631,
title = {Linearizability Criteria for Systems of Two Second-Order Differential Equations by Complex Methods},
author = {S. Ali and F. M. Mahomed and Asghar Qadir},
journal= {arXiv preprint arXiv:1001.4631},
year = {2011}
}
Comments
published in Nonlinear Dynamics