Next Article in Journal
Generalized Circulant Matrices
Previous Article in Journal
To Re-Archive an Archive. An Experience in Art Therapy over 25 Years and 25,000 Images
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Abstract

A Geometric View on the Symmetries of Differential Equations †

1
Instituto de Ciencias Fisicas y Matematicas, Universidad Austral de Chile, Valdivia 5090000, Chile
2
Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban 4000, South Africa
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 73; https://doi.org/10.3390/proceedings2010073
Published: 4 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)
We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with n independent and m dependent variables (n × m systems). We solve the symmetry conditions in a geometric way and determine the general form of the symmetry vector and of the Noetherian conservation laws. We find geometric criteria for the existence and the derivation of the symmetries. Specifically we prove that the point symmetries are generated by the collineations of two (pseudo)metrics, which are defined in the spaces of independent and dependent variables. Applications in systems of physical interests are presented.

Share and Cite

MDPI and ACS Style

Paliathanasis, A. A Geometric View on the Symmetries of Differential Equations. Proceedings 2018, 2, 73. https://doi.org/10.3390/proceedings2010073

AMA Style

Paliathanasis A. A Geometric View on the Symmetries of Differential Equations. Proceedings. 2018; 2(1):73. https://doi.org/10.3390/proceedings2010073

Chicago/Turabian Style

Paliathanasis, Andronikos. 2018. "A Geometric View on the Symmetries of Differential Equations" Proceedings 2, no. 1: 73. https://doi.org/10.3390/proceedings2010073

Article Metrics

Back to TopTop