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title:
 
Provenance of Type II hidden symmetries from nonlinear partial differential equations
publication:
 
JNMP
volume-issue:   13 - 4
pages:   612 - 622
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.2006.13.4.12 (how to use a DOI)
author(s):
 
Barbara ABRAHAM-SHRAUNER, Keshlan S GOVINDER
publication date:
 
November 2006
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:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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