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Symmetries play an critical role in finding analytic solutions to nonlineardifferential equations. A symmetry is a mapping of the solutions of thedifferential equation into the solutions and have been studied extensively forover a century. We present a computational approach to finding symmetries andcomputer algebra programs to compute the usually very large system ofdetermining partial differential equations. We also provide computer algebraalgorithm that at least automatically solves most of these equations and insimple cases provides a complete solution. The algorithms are programmed inmaxima/wxmaxima that is freely available.

Practical Guide to the Symbolic Computation of Symmetries of Differential Equations