Programs for Applying Symmetries of PDEs

In this paper the programs APPLYSYM, QUASILINPDE and DETRAFO are described which aim at the utilization of infinitesimal symmetries of differential equations. The purpose of QUASILINPDE is the general solution of quasilinear PDEs. This procedure is used by APPLYSYM for the application of point symmetries for either • calculating similarity variables to perform a point transformation which lowers the order of an ODE or effectively reduces the number of explicitly occuring independent variables in a PDE(-system) or for • generalizing given special solutions of ODEs / PDEs with new constant parameters. The program DETRAFO performs arbitrary pointand contact transformations of ODEs / PDEs and is applied if similarity and symmetry variables have been found. The program APPLYSYM is used in connection with the program LIEPDE for formulating and solving the conditions for pointand contact symmetries which is described in [4]. The actual problem solving is done in all these programs through a call to the package CRACK for solving overdetermined PDE-systems.