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Media type:
E-Article
Title:
Some relations between symmetries of nonlocally related systems
Contributor:
Yang, Zhengzheng;
Cheviakov, Alexei F.
Published:
AIP Publishing, 2014
Published in:
Journal of Mathematical Physics, 55 (2014) 8
Language:
English
DOI:
10.1063/1.4891491
ISSN:
0022-2488;
1089-7658
Origination:
Footnote:
Description:
The paper is concerned with relations between local symmetries of systems of partial differential equations (PDE) within trees of nonlocally related PDE systems. It is shown that potential systems arising from a given system through linearly independent conservation laws are nonlocally related to each other. Further, a theorem is proven stating that for a PDE system which has precisely n linearly independent local conservation laws, any local symmetry of the PDE system is a projection of some local symmetry of the n-plet potential system. Moreover, a criterion is presented to determine whether or not a specific local symmetry of a given PDE system is a projection of some local symmetry of a specific potential system. Examples are considered. Finally, a formula for a symmetry of a given PDE system in terms of a local symmetry of a nonlocally related subsystem is given. The formula can be used to determine whether a symmetry of the subsystem yields a local or a nonlocal symmetry of the given system, without the need to undertake a full symmetry classification and comparison between the given system and the subsystem.