Hindawi Publishing Corporation
Journal of Applied Mathematics
Volume 2013, Article ID 439767, 1 page
http://dx.doi.org/10.1155/2013/439767
Editorial
Symmetries, Differential Equations, and
Applications: Galois Bicentenary
Fazal M. Mahomed,1 Asghar Qadir,1,2 and Mehmet Pakdemirli3
1
Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics,
University of the Witwatersrand, Wits 2050, South Africa
2
Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad, Pakistan
3
Applied Mathematics and Computation Center, Celal Bayar University, 45040 Manisa, Turkey
Correspondence should be addressed to Fazal M. Mahomed; fazal.mahomed@wits.ac.za
Received 3 June 2013; Accepted 3 June 2013
Copyright © 2013 Fazal M. Mahomed et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
This special issue commemorated the bicentenary of the birth
of Évariste Galois who introduced the notion of a group and
made fundamental contributions to the solution of polynomial equations. The formal mathematical concept of symmetry thus came from Galois theory. Symmetry was inaugurated
and utilized in the solution of differential equations by Sophus
Lie in the 1870s. The algebraic approach has thus become of
great importance in the theory and applications of differential
equations. There was a recent Conference SDEA2012 on this
topic held in Johannesburg from 23 to 27 January, 2012.
SDEA2012 brought together researchers from all over the
world to exchange ideas, share their research findings, and
identify future research directions in symmetry and its manifold applications.
We invited the conference participants and researchers in
the field to contribute original research articles and reviews
to this special issue. We received many contributions which
ranged from ordinary to partial differential equations as well
as applications. There was one review article on geometric linearization by one of the editors, Asghar Qadir, which covered
the state of work in this interesting aspect. The topics of the
papers included the following:
(i) Lie theory in approximate and complex differential
equations,
(ii) Noether symmetries and their extensions,
(iii) other methods for first integrals and conservation
laws,
(iv) linearization,
(v) classification schemes,
(vi) invariant characterization,
(vii) stochastic differential equations,
(viii) geometrical methods,
(ix) computational mathematics,
(x) classical mechanics, continuum mechanics, and general relativity,
(xi) equations of finance,
(xii) mathematical modeling in the applied sciences and
engineering.
Acknowledgments
We express our sincere appreciation to the authors for their
valuable contributions. Also the crucial work of all the
reviewers is greatly acknowledged.
Fazal M. Mahomed
Asghar Qadir
Mehmet Pakdemirli
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