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

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

2010-01-26

arxiv.org/abs/1001.4631v3

Mathematics

Classical Analysis and ODEs

published in Nonlinear Dynamics

Scientific paper

10.1007/s11071-010-9912-2

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.

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