KRASILSHCHIK, Iosif Semjonovich and Petr VOJČÁK. On the algebra of nonlocal symmetries for the 4D Martínez Alonso-Shabat equation. Journal of Geometry and Physics. Amsterdam: Elsevier B.V., 2021, vol. 163, may, p. "104122-1"-"104122-12", 12 pp. ISSN 0393-0440. Available from: https://dx.doi.org/10.1016/j.geomphys.2021.104122.
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Basic information
Original name On the algebra of nonlocal symmetries for the 4D Martínez Alonso-Shabat equation
Authors KRASILSHCHIK, Iosif Semjonovich (643 Russian Federation, guarantor) and Petr VOJČÁK (203 Czech Republic, belonging to the institution).
Edition Journal of Geometry and Physics, Amsterdam, Elsevier B.V. 2021, 0393-0440.
Other information
Original 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
WWW Journal of Geometry and Physics
RIV identification code RIV/47813059:19610/21:A0000098
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1016/j.geomphys.2021.104122
UT WoS 000636084800017
Keywords in English 4D Martinez Alonso-Shabat equation; Universal hierarchy equation; Lax pairs; Differential coverings; Nonlocal symmetries
Tags MÚ
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 29/3/2022 12:39.
Abstract
We consider the 4D Martinez Alonso-Shabat equation epsilon u(ty) = u(z)u(xy) - u(y)u(xz) (also referred to as the universal hierarchy equation) and using its known Lax pair construct two infinite-dimensional differential coverings over epsilon. In these coverings, we give a complete description of the Lie algebras of nonlocal symmetries. In particular, our results generalize the ones obtained in Morozov and Sergyeyev (2014) and contain the constructed there infinite hierarchy of commuting symmetries as a subalgebra in a much bigger Lie algebra.
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