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The role of symmetries in solving differential equations

โœ Scribed by M.C. Nucci

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
1020 KB
Volume
25
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

review of the role of symmetries in solving differential equations is presented. After showing some recent results on the application of classical Lie point symmetries to problems in fluid draining, meteorology, and epidemiology of AIDS, the nonclassical symmetries method is presented. Finally, it is shown that iterations of the nonclassical symmetries method yield new nonlinear equations, which inherit the Lie symmetry algebra of the given equation. Invariant solutions of these equations supply new solutions of the original equation. Furthermore, the equations yield both partial symmetries 8s given by Vorobev, and differential constraints as given by Vorobev and by Olver. Some examples are given. The importance of using ad hoc interactive REDUCE programs is underlined.

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