Volume 18, Issue Supplement 1, September 2011, Pages 135 - 142
On the Non-Inheritance of Symmetries of Partial Differential Equations
Authors
Keshlan S. Govinder*, Barbara Abraham-Shrauner†
*Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa,govinder@ukzn.ac.za
†Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, 63130, USA,bas@ese.wustl.edu
Received 12 October 2010, Accepted 3 November 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001325How to use a DOI?
- Keywords
- Lie symmetries; hidden symmetries; Lie algebras; partial differential equations; group invariant solutions
- Abstract
The inheritance of symmetries of partial differential equations occurs in a different manner from that of ordinary differential equations. In particular, the Lie algebra of the symmetries of a partial differential equation is not sufficient to predict the symmetries that will be inherited by a resulting reduced partial (or ordinary) differential equation. We show how this suggests a possible source of Type I hidden symmetries of partial differential equations as well as provide interesting consequences for solutions of partial differential equations.
- 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 - Keshlan S. Govinder AU - Barbara Abraham-Shrauner PY - 2021 DA - 2021/01/07 TI - On the Non-Inheritance of Symmetries of Partial Differential Equations JO - Journal of Nonlinear Mathematical Physics SP - 135 EP - 142 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001325 DO - 10.1142/S1402925111001325 ID - Govinder2021 ER -