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

Partha Guha; A. Ghose Choudhury; Barun Khanra; Peter G.L. Leach

doi:10.20537/nd220107

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

Partha Guha
, A. Ghose Choudhury
, Barun Khanra
, Peter G.L. Leach

Mathematics

Diamond Harbour Women’s University
Sailendra Sircar Vidyalaya
University of Cyprus
University of KwaZulu-Natal

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

2 Scopus citations

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.

Original language	British English
Pages (from-to)	103-118
Number of pages	16
Journal	Russian Journal of Nonlinear Dynamics
Volume	18
Issue number	1
DOIs	https://doi.org/10.20537/nd220107
State	Published - 2022

Keywords

Jacobi equation
nonlocal first integrals
Painlevé – Gambier
Sundman transformation
symmetry

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10.20537/nd220107

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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",

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T1 - Nonlocal Constants of Motions of Equations of Painlevé – Gambier Type and Generalized Sundman Transformation

AU - Guha, Partha

AU - Choudhury, A. Ghose

AU - Khanra, Barun

AU - Leach, Peter G.L.

N1 - Funding Information: We wish to thank Basil Grammaticos for enlightening discussions regarding the Painlevé – 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: © 2022 Institute of Computer Science Izhevsk. All rights reserved.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Jacobi equation

KW - nonlocal first integrals

KW - Painlevé – Gambier

KW - Sundman transformation

KW - symmetry

UR - https://www.scopus.com/pages/publications/85130986499

U2 - 10.20537/nd220107

DO - 10.20537/nd220107

M3 - Article

AN - SCOPUS:85130986499

SN - 2658-5324

VL - 18

SP - 103

EP - 118

JO - Russian Journal of Nonlinear Dynamics

JF - Russian Journal of Nonlinear Dynamics

IS - 1

ER -

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

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