@article{02762e0b3f4d4edaa77cae5cb82b8cb4,
title = "Nonlocal Constants of Motions of Equations of Painlev{\'e} – Gambier Type and Generalized Sundman Transformation",
abstract = "We describe a method to generate nonlocal constants of motion for a special class of nonlinear ODEs. We employ the method of the generalized Sundman transformation to obtain certain new nonlocal first integrals of autonomous second-order ordinary differential equations belonging to the classification scheme developed by Painlev{\'e} and Gambier.",
keywords = "Jacobi equation, nonlocal first integrals, Painlev{\'e} – Gambier, Sundman transformation, symmetry",
author = "Partha Guha and Choudhury, \{A. Ghose\} and Barun Khanra and Leach, \{Peter G.L.\}",
note = "Funding Information: We wish to thank Basil Grammaticos for enlightening discussions regarding the Painlev{\'e} – Gambier equations. The work of the author PG was supported by the Khalifa University of Science and Technology under grant number FSU-2021-014. PGLL thanks the Department of Mathematics and Statistics of the University of Cyprus for its generous provision of facilities and furthermore thanks the University of KwaZulu-Natal and the National Research Foundation of South Africa for their continued support. The opinions expressed in this paper should not be construed as being those of either institution. Publisher Copyright: {\textcopyright} 2022 Institute of Computer Science Izhevsk. All rights reserved.",
year = "2022",
doi = "10.20537/nd220107",
language = "British English",
volume = "18",
pages = "103--118",
journal = "Russian Journal of Nonlinear Dynamics",
issn = "2658-5324",
publisher = "Institute of Computer Science Izhevsk",
number = "1",
}