title: |
New Symmetry Reductions for some Ordinary Differential Equations |
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publication: |
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| volume-issue: | 9 - Supplement 1 | |
| pages: | 47 - 58 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2002.9.s1.4 (how to use a DOI) | |
author(s): |
M L GANDARIAS, E MEDINA, C MURIEL |
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publication date: |
February 2002 |
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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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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |