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Open AccessArticle

Comparison of Noether Symmetries and First Integrals of Two-Dimensional Systems of Second Order Ordinary Differential Equations by Real and Complex Methods

1
School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology, Campus H-12, Islamabad 44000, Pakistan
2
School of Natural Sciences (SNS),National University of Sciences and Technology, Campus H-12, Islamabad 44000, Pakistan
3
Department of Basic Sciences & Humanities, College of E & ME, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1180; https://doi.org/10.3390/sym11091180
Received: 27 June 2019 / Revised: 12 August 2019 / Accepted: 19 August 2019 / Published: 17 September 2019
(This article belongs to the Special Issue Noether's Theorem and Symmetry)
Noether symmetries and first integrals of a class of two-dimensional systems of second order ordinary differential equations (ODEs) are investigated using real and complex methods. We show that first integrals of systems of two second order ODEs derived by the complex Noether approach cannot be obtained by the real methods. Furthermore, it is proved that a complex method can be extended to larger systems and higher order. View Full-Text
Keywords: systems of ODEs; Noether operators; Noether symmetries; first integrals systems of ODEs; Noether operators; Noether symmetries; first integrals
MDPI and ACS Style

Safdar, M.; Qadir, A.; Farooq, M.U. Comparison of Noether Symmetries and First Integrals of Two-Dimensional Systems of Second Order Ordinary Differential Equations by Real and Complex Methods. Symmetry 2019, 11, 1180.

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