Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis
Joint Authors
Qadir, Asghar
Ali, S.
Safdar, M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-20
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables.
An “optimal (or simplest) canonical form” of linear systems had been established to obtain the symmetry structure, namely, with 5-, 6-, 7-, 8-, and 15-dimensional Lie algebras.
For those systems that arise from a scalar complex second-order ordinary differential equation, treated as a pair of real ordinary differential equations, we provide a “reduced optimal canonical form.” This form yields three of the five equivalence classes of linearizable systems of two dimensions.
We show that there exist 6-, 7-, and 15-dimensional algebras for these systems and illustrate our results with examples.
American Psychological Association (APA)
Safdar, M.& Qadir, Asghar& Ali, S.. 2011. Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-17.
https://search.emarefa.net/detail/BIM-451611
Modern Language Association (MLA)
Safdar, M.…[et al.]. Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis. Mathematical Problems in Engineering No. 2011 (2011), pp.1-17.
https://search.emarefa.net/detail/BIM-451611
American Medical Association (AMA)
Safdar, M.& Qadir, Asghar& Ali, S.. Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-17.
https://search.emarefa.net/detail/BIM-451611
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-451611