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Symmetries and differential equations

1981; Institute of Physics; Volume: 14; Issue: 8 Linguagem: Inglês

10.1088/0305-4470/14/8/015

1361-6447

Jehuda Meinhardt,

Optics and Image Analysis

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.