Symmetries and differential equations
- 1 August 1981
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 14 (8) , 1893-1914
- https://doi.org/10.1088/0305-4470/14/8/015
Abstract
The knowledge of the maximal Lie group or abstract monoid of symmetries of an ordinary non-singular differential equation (or system of equations) allows us to obtain solutions of them. Traditional similarity analysis of point transformations is extended to non-point transformations (inclusion of derivatives), giving analytic expressions for solutions, where previously only numerical methods were used. Examples are given, and the didactic aspect is emphasised.Keywords
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