Simple and collective twisted symmetries
Research partially supported by MIUR-PRIN program under project 2010-JJ4KPA
- https://doi.org/10.1080/14029251.2014.975530How to use a DOI?
- Symmetry, Differential Equations
After the introduction of λ -symmetries by Muriel and Romero, several other types of so called “twisted symmetries” have been considered in the literature (their name refers to the fact they are defined through a deformation of the familiar prolongation operation); they are as useful as standard symmetries for what concerns symmetry reduction of ODEs or determination of special (invariant) solutions for PDEs and have thus attracted attention. The geometrical relation of twisted symmetries to standard ones has already been noted: for some type of twisted symmetries (in particular, λ and µ-symmetries), this amounts to a certain kind of gauge transformation.
In a previous review paper  we have surveyed the first part of the developments of this theory; in the present paper we review recent developments. In particular, we provide a unifying geometrical description of the different types of twisted symmetries; this is based on the classical Frobenius reduction applied to distribution generated by Lie-point (local) symmetries.
- © 2014 The Authors. Published by Atlantis Press and Taylor & Francis
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- 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 - G. Gaeta PY - 2021 DA - 2021/01 TI - Simple and collective twisted symmetries JO - Journal of Nonlinear Mathematical Physics SP - 593 EP - 627 VL - 21 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2014.975530 DO - https://doi.org/10.1080/14029251.2014.975530 ID - Gaeta2021 ER -