Auxiliary functions for rational ODEs with 2 and 3 singular values

We examine auxiliary functions which are related to certain second order nonlinear differential equations with 2 and 3 singular values. The auxiliary functions satisfy first order linear differential equations. It is shown that after imposing suitable conditions on the coefficients of the linear equ...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 597; no. 1; pp. 12036 - 12044
Main Author Filipuk, G
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 13.04.2015
Subjects
Linear equations
Mathematical analysis
Nonlinear differential equations
Physics
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ISSN1742-6588
1742-6596
1742-6596
DOI10.1088/1742-6596/597/1/012036

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Summary:We examine auxiliary functions which are related to certain second order nonlinear differential equations with 2 and 3 singular values. The auxiliary functions satisfy first order linear differential equations. It is shown that after imposing suitable conditions on the coefficients of the linear equations and on the form of the auxiliary functions one can reduce the nonlinear differential equations to the (modified) third and fifth Painlevé equations and the fourth Painlevé equation.
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ISSN:1742-6588
1742-6596
1742-6596
DOI:10.1088/1742-6596/597/1/012036