On the links between some generalized Pinney and nonlinear Gambier equations (Q1301886)
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scientific article; zbMATH DE number 1334735
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the links between some generalized Pinney and nonlinear Gambier equations |
scientific article; zbMATH DE number 1334735 |
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On the links between some generalized Pinney and nonlinear Gambier equations (English)
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12 September 1999
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Two cases of the differential equation \(u_{xx}+w(x)u=ku^{-3}+ P(u_x,u)\), \(k\) constant, are treated: \(P(u_x,u)= -6u_xu^4-u^9\) and \(P(u_x,u)=-8u_x u^2-4u^5\). By transformations \(u=y^{1/4}\) and \(y^{1/2}\), respectively, the author links them with two second-order nonlinear differential equations which are linearizable and which possess the Painlevé property.
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generalized Pinney and nonlinear Gambier equations
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second-order nonlinear differential equations
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Painlevé property
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