Linearizability criteria for systems of two second-order differential equations by complex methods

作者：Ali S^*; Mahomed F M; Qadir Asghar

来源：Nonlinear Dynamics, 2011, 66(1-2): 77-88.

DOI：10.1007/s11071-010-9912-2

• Complex linearization
• Complex Lie symmetries
• Lie linearizability

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.

• 出版日期2011-10