Conditional linearizability criteria for a system of third-order ordinary differential equations

Fazal M. Mahomed; I. Naeem; Asghar Qadir

doi:10.1016/j.nonrwa.2008.09.021

Conditional linearizability criteria for a system of third-order ordinary differential equations

Fazal M. Mahomed^*, I. Naeem, Asghar Qadir

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

9 Scopus citations

Abstract

We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.

Original language	English
Pages (from-to)	3404-3412
Number of pages	9
Journal	Nonlinear Analysis: Real World Applications
Volume	10
Issue number	6
DOIs	https://doi.org/10.1016/j.nonrwa.2008.09.021
State	Published - Dec 2009

Bibliographical note

Funding Information:
AQ is most grateful to DECMA and the School of Computational and Applied Mathematics, University of the Witwatersrand and for some useful comments by Profs. P. Leach, S. Meleshko and R. Popovych. IN thanks the School of CAM, the University of the Witwatersrand and the NRF for financial support.

Keywords

Geodesic equation
Linearization criteria
System of third-order ordinary differential equations

ASJC Scopus subject areas

Analysis
General Engineering
General Economics, Econometrics and Finance
Computational Mathematics
Applied Mathematics

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10.1016/j.nonrwa.2008.09.021

Cite this

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title = "Conditional linearizability criteria for a system of third-order ordinary differential equations",

abstract = "We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.",

keywords = "Geodesic equation, Linearization criteria, System of third-order ordinary differential equations",

author = "Mahomed, \{Fazal M.\} and I. Naeem and Asghar Qadir",

note = "Funding Information: AQ is most grateful to DECMA and the School of Computational and Applied Mathematics, University of the Witwatersrand and for some useful comments by Profs. P. Leach, S. Meleshko and R. Popovych. IN thanks the School of CAM, the University of the Witwatersrand and the NRF for financial support. ",

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language = "English",

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journal = "Nonlinear Analysis: Real World Applications",

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T1 - Conditional linearizability criteria for a system of third-order ordinary differential equations

AU - Mahomed, Fazal M.

AU - Naeem, I.

AU - Qadir, Asghar

N1 - Funding Information: AQ is most grateful to DECMA and the School of Computational and Applied Mathematics, University of the Witwatersrand and for some useful comments by Profs. P. Leach, S. Meleshko and R. Popovych. IN thanks the School of CAM, the University of the Witwatersrand and the NRF for financial support.

PY - 2009/12

Y1 - 2009/12

N2 - We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.

AB - We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.

KW - Geodesic equation

KW - Linearization criteria

KW - System of third-order ordinary differential equations

UR - https://www.scopus.com/pages/publications/68849122186

U2 - 10.1016/j.nonrwa.2008.09.021

DO - 10.1016/j.nonrwa.2008.09.021

M3 - Article

AN - SCOPUS:68849122186

SN - 1468-1218

VL - 10

SP - 3404

EP - 3412

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 6

ER -

Conditional linearizability criteria for a system of third-order ordinary differential equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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