Volume 9, Issue Supplement 1, February 2002, Pages 47 - 58
New Symmetry Reductions for some Ordinary Differential Equations
M L GANDARIAS, E MEDINA, C MURIEL
M L GANDARIAS
Received 30 April 2001, Revised 17 July 2001, Accepted 26 July 2001, Available Online 1 February 2002.
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- 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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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 -