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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F24%3AA0000160" target="_blank" >RIV/47813059:19610/24:A0000160 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00023-024-01425-2" target="_blank" >https://link.springer.com/article/10.1007/s00023-024-01425-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00023-024-01425-2" target="_blank" >10.1007/s00023-024-01425-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annales Henri Poincaré

ISSN

1424-0637

e-ISSN

1424-0661

Svazek periodika

25

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

37

Strana od-do

4633-4669

Kód UT WoS článku

001172954900001

EID výsledku v databázi Scopus

2-s2.0-85186432738