Nonlocal Extensions of Similarity Methods

DOI

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.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - George Bluman
PY  - 2008
DA  - 2008/08/01
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  - 10.2991/jnmp.2008.15.s1.1
ID  - Bluman2008
ER  -