Journal of Nonlinear Mathematical Physics

Volume 16, Issue 4, March 2013, Pages 489 - 504

On Nonlocal Symmetries, Nonlocal Conservation Laws and Nonlocal Transformations of Evolution Equations: Two Linearisable Hierarchies

Authors
Norbert Euler*, Marianna Euler
Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
Corresponding Author
Norbert Euler
Received 22 February 2009, Accepted 31 March 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925109000509How to use a DOI?
Keywords
Nonlocal symmetries, conservation laws, linearisation, integrable hierarchies, nonlinear evolution equations
Abstract

We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal conservation laws and nonlocal transformations for the equations. We demonstrate our approach and derive second degree potential symmetries for the Burgers' hierarchy and the Calogero–Degasperis–Ibragimov–Shabat hierarchy.

Copyright
© 2009 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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 4
Pages
489 - 504
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925109000509How to use a DOI?
Copyright
© 2009 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  - Norbert Euler
AU  - Marianna Euler
PY  - 2021
DA  - 2021/01
TI  - On Nonlocal Symmetries, Nonlocal Conservation Laws and Nonlocal Transformations of Evolution Equations: Two Linearisable Hierarchies
JO  - Journal of Nonlinear Mathematical Physics
SP  - 489
EP  - 504
VL  - 16
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000509
DO  - https://doi.org/10.1142/S1402925109000509
ID  - Euler2021
ER  -