A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

A MATHEMATICA package for finding Lie symmetries of partial differential equations is presented. The package is designed to create and solve the associated determining system of equations, the full set of solutions of which generates the widest permissible local Lie group of point symmetry transformations. Examples illustrating the functionality of the package's tools are given. The results of the package application to performing a full Lie group analysis of coupled nonlinear Schrödinger equations from nonlinear fiber optics are presented. Comparisons with earlier published computer algebra implementations of the Lie group method are discussed.