On Recursion Operators for Full-Fledged Nonlocal Symmetries of
the Reduced Quasi-classical Self-dual Yang-Mills Equation

J 2024

On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang-Mills Equation

JAHNOVÁ, Jiřina and Petr VOJČÁK

Basic information

Original name

On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang-Mills Equation

Authors

JAHNOVÁ, Jiřina (203 Czech Republic, belonging to the institution) and Petr VOJČÁK (203 Czech Republic, guarantor, belonging to the institution)

Edition

Annales Henri Poincaré, Cham (SW), Springer International Publishing, 2024, 1424-0637

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Switzerland

Confidentiality degree

is not subject to a state or trade secret

References:

Annales Henri Poincaré

Impact factor

Impact factor: 1.300

RIV identification code

RIV/47813059:19610/24:A0000160

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1007/s00023-024-01425-2

UT WoS

001172954900001

EID Scopus

2-s2.0-85186432738

Keywords in English

The reduced quasi-classical self-dual Yang-Mills equation; Lax pairs; coverings; recursion operators; nonlocal symmetries

Abstract

In the original language

We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang–Mills equation. It turns out that the discovered recursion operators can be interpreted as infinite-dimensional matrices of differential functions which act on the generating vector functions of the nonlocal symmetries simply by matrix multiplication. To the best of our knowledge, there are no other examples of such recursion operators in the literature so far, so our approach is completely innovative. Further, we investigate the algebraic properties of the discovered operators and discuss the R-algebra structure on the set of all recursion operators for full-fledged nonlocal symmetries of the equation in question. Finally, we illustrate the action of the obtained recursion operators on particularly chosen full-fledged symmetries and emphasize their advantages compared to the action of traditionally used recursion operators for shadows.

Cite

JAHNOVÁ, Jiřina and Petr VOJČÁK. On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang-Mills Equation. Annales Henri Poincaré. Cham (SW): Springer International Publishing, 2024, vol. 25, No 10, p. 4633-4669. ISSN 1424-0637. Available from: https://doi.org/10.1007/s00023-024-01425-2.

@article{82504,
   author = {Jahnová, Jiřina and Vojčák, Petr},
   article_location = {Cham (SW)},
   article_number = {10},
   doi = {https://doi.org/10.1007/s00023-024-01425-2},
   keywords = {The reduced quasi-classical self-dual Yang-Mills equation; Lax pairs; coverings; recursion operators; nonlocal symmetries},
   language = {eng},
   issn = {1424-0637},
   journal = {Annales Henri Poincaré},
   title = {On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang-Mills Equation},
   url = {https://link.springer.com/article/10.1007/s00023-024-01425-2},
   volume = {25},
   year = {2024}
}

TY  - JOUR
ID  - 82504
AU  - Jahnová, Jiřina - Vojčák, Petr
PY  - 2024
TI  - On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang-Mills Equation
JF  - Annales Henri Poincaré
VL  - 25
IS  - 10
SP  - 4633-4669
EP  - 4633-4669
PB  - Springer International Publishing
SN  - 14240637
KW  - The reduced quasi-classical self-dual Yang-Mills equation
KW  - Lax pairs
KW  - coverings
KW  - recursion operators
KW  - nonlocal symmetries
UR  - https://link.springer.com/article/10.1007/s00023-024-01425-2
N2  - We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang–Mills equation. It turns out that the discovered recursion operators can be interpreted as infinite-dimensional matrices of differential functions which act on the generating vector functions of the nonlocal symmetries simply by matrix multiplication. To the best of our knowledge, there are no other examples of such recursion operators in the literature so far, so our approach is completely innovative. Further, we investigate the algebraic properties of the discovered operators and discuss the R-algebra structure on the set of all recursion operators for full-fledged nonlocal symmetries of the equation in question. Finally, we illustrate the action of the obtained recursion operators on particularly chosen full-fledged symmetries and emphasize their advantages compared to the action of traditionally used recursion operators for shadows.
ER  -

JAHNOVÁ, Jiřina and Petr VOJČÁK. On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang-Mills Equation. \textit{Annales Henri Poincaré}. Cham (SW): Springer International Publishing, 2024, vol.~25, No~10, p.~4633-4669. ISSN~1424-0637. Available from: https://doi.org/10.1007/s00023-024-01425-2.

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