Volume 16, Issue 4, December 2009, Pages 489 - 504
On Nonlocal Symmetries, Nonlocal Conservation Laws and Nonlocal Transformations of Evolution Equations: Two Linearisable Hierarchies
Received 22 February 2009, Accepted 31 March 2009, Available Online 7 January 2021.
- DOI
- 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/).
Cite this article
TY - JOUR AU - Norbert Euler AU - Marianna Euler PY - 2021 DA - 2021/01/07 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 - 10.1142/S1402925109000509 ID - Euler2021 ER -