Introduction to symmetry methods in the solution of differential equations that occur in chemistry and chemical biology

This article is a short overview of the main ways in which symmetries can be used to obtain exact information about differential equations. It is written for a general scientific audience; readers do not need any previous knowledge of symmetry methods. The information yielded by symmetry methods may include the general solution of a given differential equation, special “invariant solutions” (such as similarity solutions), and conservation laws. Several symmetry methods have been implemented as computer algebra packages, which can be used by nonspecialists. Toward the end of the study, there is a brief outline of some recent developments in symmetry methods that await translation into symbolic algebra.