Computer algebra application for determining Lie and Lie-Bäcklund symmetries of differential equations

The application of computer algebra for determining Lie and Lie-Bäcklund (LB) symmetries of differential equations is considered. Algorithms for calculating the symmetries are developed and implemented on the basis of computer algebra systems REDUCE, AMP and FORMAC. The most effective and advanced program is written in FORMAC. It finds LB symmetries completely automatically. In many cases the program yields the full algebra of symmetries. If the program fails in full integration of the determining system, it reduces the remaining determining equations to the system in involution