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Russian Journal of Nonlinear Dynamics, 2022, Volume 18, Number 1, Pages 103–118
DOI: https://doi.org/10.20537/nd220107 (Mi nd781) 		 
Mathematical problems of nonlinearity

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

P. Guhaa, A. G. Choudhuryb, B. Khanrac, P. G. L. Leachde

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
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DOI: https://doi.org/10.20537/nd220107
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.
Received: 19.10.2021
Accepted: 28.01.2022
Bibliographic databases:
Document Type: Article
MSC: 34C14, 34C20
Language: english
Citation: 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., 18:1 (2022), 103–118
Citation in format AMSBIB
\Bibitem{GuhGhoKha22}
\by P. Guha, A. G. Choudhury, B. Khanra, P. G. L. Leach
\paper Nonlocal Constants of Motions of Equations
of Painlevé – Gambier Type and Generalized Sundman
Transformation
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 1
\pages 103--118
\mathnet{http://mi.mathnet.ru/nd781}
\crossref{https://doi.org/10.20537/nd220107}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4403288}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85130986499}
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