Premium
Introduction to symmetry methods in the solution of differential equations that occur in chemistry and chemical biology
Author(s) -
Hydon Peter E.
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20749
Subject(s) - homogeneous space , symmetry (geometry) , symbolic computation , invariant (physics) , similarity (geometry) , algebra over a field , differential equation , conservation law , computer science , mathematical physics , theoretical physics , mathematics , physics , pure mathematics , quantum mechanics , mathematical analysis , artificial intelligence , geometry , image (mathematics)
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. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006