Nonlocal symmetries, conservation laws, and recursion operators
of the Veronese web equation

J 2019

Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

VOJČÁK, Petr; Oleg I. MOROZOV and Iosif S. KRASIL'SHCHIK

Basic information

Original name

Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

Authors

VOJČÁK, Petr (203 Czech Republic, belonging to the institution); Oleg I. MOROZOV (643 Russian Federation) and Iosif S. KRASIL'SHCHIK (643 Russian Federation)

Edition

Journal of Geometry and Physics, Amsterdam, Elsevier B.V. 2019, 0393-0440

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

is not subject to a state or trade secret

References:

Journal of Geometry and Physics

Impact factor

Impact factor: 1.056

RIV identification code

RIV/47813059:19610/19:A0000054

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1016/j.geomphys.2019.103519

UT WoS

000496342600020

EID Scopus

2-s2.0-85072716069

Keywords in English

Veronese web equation; Differential coverings; Lax pairs; Nonlocal symmetries; Recursion operators; Master symmetries

Links

EF16_027/0008521, research and development project.

Changed: 20/4/2020 16:00, Mgr. Aleš Ryšavý

Abstract

In the original language

We study the Veronese web equation u(y)u(tx) + lambda u(x)u(ty) - (lambda + 1)u(t)u(xy) = 0 and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In the infinite differential coverings associated to these series, we describe the Lie algebras of the corresponding nonlocal symmetries. Finally, we construct a recursion operator and explore its action on nonlocal shadows. The operator provides a new shadow which serves as a master-symmetry.

Cite

VOJČÁK, Petr; Oleg I. MOROZOV and Iosif S. KRASIL'SHCHIK. Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation. Journal of Geometry and Physics. Amsterdam: Elsevier B.V., 2019, vol. 146, December, p. "103519-1"-"103519-11", 11 pp. ISSN 0393-0440. Available from: https://doi.org/10.1016/j.geomphys.2019.103519.

@article{32743,
   author = {Vojčák, Petr and Morozov, Oleg I. and Krasil'shchik, Iosif S.},
   article_location = {Amsterdam},
   article_number = {December},
   doi = {https://doi.org/10.1016/j.geomphys.2019.103519},
   keywords = {Veronese web equation; Differential coverings; Lax pairs; Nonlocal symmetries; Recursion operators; Master symmetries},
   language = {eng},
   issn = {0393-0440},
   journal = {Journal of Geometry and Physics},
   title = {Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation},
   url = {https://www.sciencedirect.com/science/article/pii/S0393044019302013?via%3Dihub},
   volume = {146},
   year = {2019}
}

TY  - JOUR
ID  - 32743
AU  - Vojčák, Petr - Morozov, Oleg I. - Krasil'shchik, Iosif S.
PY  - 2019
TI  - Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation
JF  - Journal of Geometry and Physics
VL  - 146
IS  - December
SP  - "103519-1"-"103519-11"
EP  - "103519-1"-"103519-11"
PB  - Elsevier B.V.
SN  - 03930440
KW  - Veronese web equation
KW  - Differential coverings
KW  - Lax pairs
KW  - Nonlocal symmetries
KW  - Recursion operators
KW  - Master symmetries
UR  - https://www.sciencedirect.com/science/article/pii/S0393044019302013?via%3Dihub
L2  - https://www.sciencedirect.com/science/article/pii/S0393044019302013?via%3Dihub
N2  - We study the Veronese web equation u(y)u(tx) + lambda u(x)u(ty) - (lambda + 1)u(t)u(xy) = 0 and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In the infinite differential coverings associated to these series, we describe the Lie algebras of the corresponding nonlocal symmetries. Finally, we construct a recursion operator and explore its action on nonlocal shadows. The operator provides a new shadow which serves as a master-symmetry.
ER  -

VOJČÁK, Petr; Oleg I. MOROZOV and Iosif S. KRASIL'SHCHIK. Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation. \textit{Journal of Geometry and Physics}. Amsterdam: Elsevier B.V., 2019, vol.~146, December, p.~''103519-1''-''103519-11'', 11 pp. ISSN~0393-0440. Available from: https://doi.org/10.1016/j.geomphys.2019.103519.

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