Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Theoretical and Mathematical Physics
ISSN
0040-5779
e-ISSN
1573-9333
Volume of the periodical
196
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
1089-1110
UT code for WoS article
000443722200001
EID of the result in the Scopus database
2-s2.0-85052680485