Solutions in closed form and as power series to the real Lorenz equations (Q2756930)
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scientific article; zbMATH DE number 1675024
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solutions in closed form and as power series to the real Lorenz equations |
scientific article; zbMATH DE number 1675024 |
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Solutions in closed form and as power series to the real Lorenz equations (English)
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19 November 2001
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Lorenz system
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Emden-Fowler equation
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Lie point symmetry
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Painlevé test
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solution in closed form
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The authors study the Lorenz nonlinear system. For the parameter values \(\sigma=0.5\), \(b=I\) and \(r=0\), the general exact solution in terms of Jacobi's elliptic functions is constructed using the Lie theory of extended groups.NEWLINENEWLINENEWLINEThen, the Painlevé properties of Lorenz's system for some values of parameters are analyzed. An appropriate extension of the Painlevé analysis provides further particular exact solutions not possessing the Painlevé property in the form of power series.
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