P. Guha, A. G. Choudhury, B. Khanra, P. G. L. Leach, “Nonlocal Constants of Motions of Equations of Painlevé – Gambier Type and Generalized Sundman Transformation”, Rus. J. Nonlin. Dyn., 2022, Volume 18, Number 1,Pages <nobr>103–118</nobr>

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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

Rus. J. Nonlin. Dyn., 2022 Volume 18, Number 1, Pages 103–118 (Mi nd781)

Mathematical problems of nonlinearity

Nonlocal Constants of Motions of Equations of Painlevé – Gambier Type and Generalized Sundman Transformation

P. Guha^a, A. G. Choudhury^b, B. Khanra^c, P. G. L. Leach^de

^a Department of Mathematics, Khalifa University of Science and Technology, Main Campus, Abu Dhabi, United Arab Emirates
^b Department of Physics, Diamond Harbour Women’s University, D. H. Road, Sarisha 743368, West Bengal, India
^c Sailendra Sircar Vidyalaya, 62A, Shyampukur Street, Kolkata-700004, India
^d School of Mathematical, Statistical, Acturial and Computer Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, Republic of South Africa
^e Department of Mathematics and Statistics, University of Cyprus, Lefkosia 1678, Cyprus

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 Painlevé and Gambier.

Keywords: Sundman transformation, Painlevé –Gambier, symmetry, nonlocal first integrals, Jacobi equation.

MSC: 34C14, 34C20

Received: 19.10.2021
Accepted: 28.01.2022

Language: english

DOI: 10.20537/nd220107

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© Steklov Math. Inst. of RAS, 2024