Provenance of Type II hidden symmetries from nonlinear partial differential equations

DOI

10.2991/jnmp.2006.13.4.12How to use a DOI?

Abstract

The provenance of Type II hidden point symmetries of differential equations reduced from nonlinear partial differential equations is analyzed. The hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a Lie point symmetry. These Type II hidden symmetries do not arise from contact symmetries or nonlocal symmetries as in the case of ordinary differential equations. The Lie point symmetries of a model equation and the two-dimensional Burgers' equation and their descendants are used to identify the hidden symmetries. The significant new result is the provenance of the Type II Lie point hidden symmetries found for differential equations reduced from partial differential equations. Two methods for determining the source of the hidden symmetries are developed.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Barbara Abraham-Shrauner
AU  - Keshlan S. Govinder
PY  - 2006
DA  - 2006/11/01
TI  - Provenance of Type II hidden symmetries from nonlinear partial differential equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 612
EP  - 622
VL  - 13
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.4.12
DO  - 10.2991/jnmp.2006.13.4.12
ID  - Abraham-Shrauner2006
ER  -