Pure imaginary solutions of the second Painlevé equation (Q1777824)
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scientific article; zbMATH DE number 2171759
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pure imaginary solutions of the second Painlevé equation |
scientific article; zbMATH DE number 2171759 |
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Pure imaginary solutions of the second Painlevé equation (English)
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25 May 2005
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The paper deals with the second Painlevé equation of the form \[ y''= 2y^3+ 2y+ i\alpha,\quad \alpha\in\mathbb{R}. \] The author proves the existence of pure imaginary solutions and their asymptotics as \(x\to\infty\) which are infinitely differentiable. Some specific cases of the equation are considered in detail.
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Painlevé equation
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asymptotic solution
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