Journal of Nonlinear Mathematical Physics

Volume 15, Issue Supplement 1, August 2008, Pages 1 - 24

Nonlocal Extensions of Similarity Methods

Authors
George Bluman
Corresponding Author
George Bluman
Available Online 1 August 2008.
DOI
https://doi.org/10.2991/jnmp.2008.15.s1.1How to use a DOI?
Abstract
Similarity methods include the calculation and use of symmetries and conservation laws for a given partial differential equation (PDE). There exists a variety of software to calculate and use local symmetries and local conservation laws. However, it is often the case that a given PDE admits no useful local symmetry or local conservation law. It is shown how to construct systematically trees of nonlocally related but equivalent systems of PDEs. A local symmetry or local conservation law of a PDE in such a tree could yield a useful nonlocal symmetry or nonlocal conservation law for a given PDE within such a tree. If this is the case, one can extend the usefulness of similarity methods for a given PDE. Many examples are given.
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - Supplement 1
Pages
1 - 24
Publication Date
2008/08
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2008.15.s1.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - George Bluman
PY  - 2008
DA  - 2008/08
TI  - Nonlocal Extensions of Similarity Methods
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 24
VL  - 15
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s1.1
DO  - https://doi.org/10.2991/jnmp.2008.15.s1.1
ID  - Bluman2008
ER  -