Journal of Nonlinear Mathematical Physics

Volume 21, Issue 4, October 2014, Pages 593 - 627

Simple and collective twisted symmetries

Authors
G. Gaeta*
Dipartimento di Matematica, Università degli Studi di Milano, via C. Saldini 50, 20133 Milano (Italy), giuseppe.gaeta@unimi.it
*

Research partially supported by MIUR-PRIN program under project 2010-JJ4KPA

Received 8 May 2014, Accepted 23 August 2014, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2014.975530How to use a DOI?
Keywords
Symmetry, Differential Equations
Abstract

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 [23] 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.

Copyright
© 2014 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
21 - 4
Pages
593 - 627
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2014.975530How to use a DOI?
Copyright
© 2014 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  - 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  -