Simple and collective twisted symmetries

DOI

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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TY  - JOUR
AU  - G. Gaeta
PY  - 2021
DA  - 2021/01/06
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  - 10.1080/14029251.2014.975530
ID  - Gaeta2021
ER  -