European Journal of Applied Mathematics

How to construct the discrete symmetries of partial differential equations

P. E. HYDON a1
a1 Department of Mathematics and Statistics, University of Surrey, Guildford GU2 5XH, UK (email:


This paper introduces an algorithm for calculating all discrete point symmetries of a given partial differential equation with a known nontrivial group of Lie point symmetries. The method enables the user to determine the discrete symmetries with little more effort than is used to find the Lie symmetries. It is used to obtain the discrete point symmetries of Burgers' equation, the spherical Burgers' equation, and the Harry–Dym equation. The method can be extended to some types of nonlocal symmetry; we derive the quasi-local discrete symmetries of a system of PDEs from gas dynamics.

(Received May 12 2000)
(Revised May 12 2000)