N ov 2 00 7 Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - I : Ordinary Differential Equations
نویسندگان
چکیده
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.
منابع مشابه
0 N ov 2 00 7 Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II : Partial Differential Equations
The linearization of complex ordinary differential equations is studied by extending Lie’s criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible comp...
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