Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F18%3AA0000024" target="_blank" >RIV/47813059:19610/18:A0000024 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1134%2FS0040577918080019" target="_blank" >https://link.springer.com/article/10.1134%2FS0040577918080019</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1134/S0040577918080019" target="_blank" >10.1134/S0040577918080019</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study

Popis výsledku v původním jazyce

We continue the study of Lax integrable equations. We consider four three-dimensional equations: (1) the rdDym equation u(ty) = u(x)u(xy) - u(y)u(xx), (2) the Pavlov equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy), (3) the universal hierarchy equation u(yy) = u(t)u(xy) - u(y)u(tx), and (4) the modified Veronese web equation u(ty) = u(t)u(xy) - u(y)u(tx). For each equation, expanding the known Lax pairs in formal series in the spectral parameter, we construct two differential coverings and completely describe the nonlocal symmetry algebras associated with these coverings. For all four pairs of coverings, the obtained Lie algebras of symmetries manifest similar (but not identical) structures; they are (semi)direct sums of the Witt algebra, the algebra of vector fields on the line, and loop algebras, all of which contain a component of finite grading. We also discuss actions of recursion operators on shadows of nonlocal symmetries.

Název v anglickém jazyce

Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study

Popis výsledku anglicky

We continue the study of Lax integrable equations. We consider four three-dimensional equations: (1) the rdDym equation u(ty) = u(x)u(xy) - u(y)u(xx), (2) the Pavlov equation u(yy) = u(tx) + u(y)u(xx) - u(x)u(xy), (3) the universal hierarchy equation u(yy) = u(t)u(xy) - u(y)u(tx), and (4) the modified Veronese web equation u(ty) = u(t)u(xy) - u(y)u(tx). For each equation, expanding the known Lax pairs in formal series in the spectral parameter, we construct two differential coverings and completely describe the nonlocal symmetry algebras associated with these coverings. For all four pairs of coverings, the obtained Lie algebras of symmetries manifest similar (but not identical) structures; they are (semi)direct sums of the Witt algebra, the algebra of vector fields on the line, and loop algebras, all of which contain a component of finite grading. We also discuss actions of recursion operators on shadows of nonlocal symmetries.

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

2018

Kód důvěrnosti údajů

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

Název periodika

Theoretical and Mathematical Physics

ISSN

0040-5779

e-ISSN

1573-9333

Svazek periodika

196

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1089-1110

Kód UT WoS článku

000443722200001

EID výsledku v databázi Scopus

2-s2.0-85052680485