J 2019

On symmetries of the Gibbons-Tsarev equation

BARAN, Hynek; Petr BLASCHKE; Michal MARVAN and Iosif S. KRASIL'SHCHIK

Basic information

Original name

On symmetries of the Gibbons-Tsarev equation

Authors

BARAN, Hynek (203 Czech Republic, belonging to the institution); Petr BLASCHKE (203 Czech Republic, belonging to the institution); Michal MARVAN (203 Czech Republic, guarantor, belonging to the institution) 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:A0000042

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1016/j.geomphys.2019.05.011

UT WoS

000481564700005

EID Scopus

2-s2.0-85066736273

Keywords in English

Gibbons-Tsarev equation; Differential coverings; Nonlocal symmetries; Nonlocal conservation laws; Witt algebra

Tags

MÚ

Tags

International impact, Reviewed

Links

EE2.3.20.0002, research and development project. GBP201/12/G028, research and development project.
Changed: 28/4/2020 19:38, Mgr. Aleš Ryšavý

Abstract

In the original language

We study the Gibbons-Tsarev equation z(yy) + z(x)z(xy) - z(y)z(xx) + 1 = 0 and, using the known Lax pair, we construct infinite series of conservation laws and the algebra of nonlocal symmetries in the covering associated with these conservation laws. We prove that the algebra is isomorphic to the Witt algebra. Finally, we show that the constructed symmetries are unique in the class of polynomial ones.
Displayed: 31/10/2025 11:02