MathLie a program of doing symmetry analysis

We discuss the capabilities of MathLie in supporting the symmetry analysis of differential equations. MathLie is a computer algebra program written in Mathematica 3.0 and capable to carry out different types of symmetry calculations for ordinary as well as for partial differential equations. MathLie determines point symmetries, non-classical symmetries, potential symmetries, approximate symmetries, and generalized symmetries for partial differential equations. Three examples, the Harry–Dyme, the turbulent burst equations, and the Zabolotskaya–Khoklov equation demonstrate the application of MathLie in connection with point symmetries. We also present similarity solutions of these equations.