Journal of Nonlinear Mathematical Physics

Volume 9, Issue Supplement 1, February 2002, Pages 47 - 58

New Symmetry Reductions for some Ordinary Differential Equations

Authors
M L GANDARIAS, E MEDINA, C MURIEL
Corresponding Author
M L GANDARIAS
Available Online 1 February 2002.
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.4How to use a DOI?
Abstract
In this work we derive potential symmetries for ordinary differential equations. By using these potential symmetries we find that the order of the ODE can be reduced even if this equation does not admit point symmetries. Moreover, in the case for which the ODE admits a group of point symmetries, we find that the potential symmetries allow us to perform further reductions than its point symmetries. Some diffusion equations admitting an infinite number of potential symmetries and the scaling group as a Lie symmetry are considered and some general results are obtained. For all the equations that we have studied, a set of potential symmetries admitted by the diffusion equation is "inherited" by the ODE that emerges as the reduced equation under the scaling group.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 100
Pages
47 - 58
Publication Date
2002/02
ISBN
91-631-2120-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.4How 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  - M L GANDARIAS
AU  - E MEDINA
AU  - C MURIEL
PY  - 2002
DA  - 2002/02
TI  - New Symmetry Reductions for some Ordinary Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 47
EP  - 58
VL  - 9
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s1.4
DO  - https://doi.org/10.2991/jnmp.2002.9.s1.4
ID  - GANDARIAS2002
ER  -