Affiliation:
1. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
2. Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain
Abstract
Nonlocally related systems, obtained through conservation law and symmetry-based methods, have proved to be useful for determining nonlocal symmetries, nonlocal conservation laws, non-invertible mappings and new exact solutions of a given partial differential equation (PDE) system. In this paper, it is shown that the symmetry-based method is a differential invariant-based method. It is shown that this allows one to naturally extend the symmetry-based method to ordinary differential equation (ODE) systems and to PDE systems with at least three independent variables. In particular, we present the situations for ODE systems, PDE systems with two independent variables and PDE systems with three or more independent variables, separately, and show that these three situations are directly connected. Examples are exhibited for each of the three situations.
Funder
Natural Sciences and Engineering Research Council of Canada
Junta de Andalucía group FQM-201
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference25 articles.
1. Similarity, Self-Similarity, and Intermediate Asymptotics
2. Bianchi L. 1918 Lezioni sulla Teoria dei Gruppi Continui Finiti di Transformazioni. Pisa, Italy: Enrico Spoerri.
3. Bluman GW, Anco SC. 2002 Symmetry and integration methods for differential equations. New York, NY: Springer.
4. Symmetries and Differential Equations
5. Applications of Lie Groups to Differential Equations