Volume 18, Issue Supplement 1, September 2011, Pages 123 - 133
Reductions for Some Ordinary Differential Equations Through Nonlocal Symmetries
Received 1 October 2010, Accepted 10 November 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001313How to use a DOI?
- Keywords
- Conditional symmetry; nonlocal symmetry; ordinary differential equation
- Abstract
In [19] we derive nonlocal symmetries for ordinary differential equations by embedding the given equation in an auxiliary system. Since the nonlocal symmetries of the ODE's are local symmetries of the associated auxiliary system this result provides an algorithmic method to derive this kind of nonlocal symmetries. In this work we show some classes of ordinary differential equations which do not admit any Lie symmetry unless some conditions are satisfied but for which we have derived nonlocal symmetries. These nonlocal symmetries allow us to reduce the order for these equations even if these equations do not admit point symmetries.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - M. L. Gandarias AU - M. S. Bruzón PY - 2021 DA - 2021/01/07 TI - Reductions for Some Ordinary Differential Equations Through Nonlocal Symmetries JO - Journal of Nonlinear Mathematical Physics SP - 123 EP - 133 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001313 DO - 10.1142/S1402925111001313 ID - Gandarias2021 ER -