On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type

Partha Guha; Barun Khanra; A. Ghose Choudhury

doi:10.1016/j.na.2009.12.004

On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type

Partha Guha, Barun Khanra, A. Ghose Choudhury

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We employ the generalized Sundman transformation method to obtain certain new first integrals of autonomous second-order ordinary differential equations belonging to the Painlevé-Gambier classification scheme. This method not only yields systematically the known first integrals of a large number of the Painlevé-Gambier equations but also some time dependent ones, which greatly simplify the computation of their corresponding solution. In addition we also compute the Sundman symmetries of these equations.

Original language	British English
Pages (from-to)	3247-3257
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	72
Issue number	7-8
DOIs	https://doi.org/10.1016/j.na.2009.12.004
State	Published - 1 Apr 2010

Keywords

First integrals
Jacobi equation
Painlevé-Gambier equations
Sundman symmetries
Sundman transformation

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10.1016/j.na.2009.12.004

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abstract = "We employ the generalized Sundman transformation method to obtain certain new first integrals of autonomous second-order ordinary differential equations belonging to the Painlev{\'e}-Gambier classification scheme. This method not only yields systematically the known first integrals of a large number of the Painlev{\'e}-Gambier equations but also some time dependent ones, which greatly simplify the computation of their corresponding solution. In addition we also compute the Sundman symmetries of these equations.",

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AU - Guha, Partha

AU - Khanra, Barun

AU - Choudhury, A. Ghose

PY - 2010/4/1

Y1 - 2010/4/1

N2 - We employ the generalized Sundman transformation method to obtain certain new first integrals of autonomous second-order ordinary differential equations belonging to the Painlevé-Gambier classification scheme. This method not only yields systematically the known first integrals of a large number of the Painlevé-Gambier equations but also some time dependent ones, which greatly simplify the computation of their corresponding solution. In addition we also compute the Sundman symmetries of these equations.

AB - We employ the generalized Sundman transformation method to obtain certain new first integrals of autonomous second-order ordinary differential equations belonging to the Painlevé-Gambier classification scheme. This method not only yields systematically the known first integrals of a large number of the Painlevé-Gambier equations but also some time dependent ones, which greatly simplify the computation of their corresponding solution. In addition we also compute the Sundman symmetries of these equations.

KW - First integrals

KW - Jacobi equation

KW - Painlevé-Gambier equations

KW - Sundman symmetries

KW - Sundman transformation

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DO - 10.1016/j.na.2009.12.004

M3 - Article

AN - SCOPUS:75449103316

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SP - 3247

EP - 3257

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 7-8

ER -

On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type

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Keywords

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