On Generalized Sundman Transformation Method, First Integrals and Solutions of Painlevé-Gambier Type Equations

Partha Guha, Anindya Ghose Choudhury, and Barun Khanra

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Submission date: 23. Jul. 2009
Pages: 28
published in: Nonlinear analysis / A, 72 (2010) 7/8, p. 3247-3257 
DOI number (of the published article): 10.1016/j.na.2009.12.004
Bibtex
MSC-Numbers: 34C14, 34C20
Keywords and phrases: Painlev\'e-Gambier, first integrals, Jacobi equation
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Abstract:
We employ generalized Sundman transformation method to

obtain certain new first integrals of autonomous second-order

ordinary differential equations belonging to the

Painlevé-Gambier classification scheme. In particular this

method yields systematically both known and unknown first

integrals of a large number of the autonomous Painlevé-Gambier equations.