Journal of Nonlinear Mathematical Physics

Volume 27, Issue 1, October 2019, Pages 36 - 56

Realizations of the Witt and Virasoro Algebras and Integrable Equations

Authors
Qing Huang
School of Mathematics, Center for Nonlinear Studies, Northwest University, Xi’an 710127, P.R. China, hqing@nwu.edu.cn
Renat Zhdanov*
CyberOptics Corporation, 5900 Golden Hills Drive, Minneapolis, MN 55416, USA, rzhdanov@cyberoptics.com
*Corresponding author.
Corresponding Author
Renat Zhdanov
Received 6 September 2018, Accepted 2 July 2019, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2020.1683964How to use a DOI?
Keywords
Witt algebra, Virasoro algebra, Lie vector field, equivalence transformation, integrable equation
Abstract

In this paper we study realizations of infinite-dimensional Witt and Virasoro algebras. We obtain a complete description of realizations of the Witt algebra by Lie vector fields of first-order differential operators over the space ℝ3. We prove that none of them admits non-trivial central extension, which means that there are no realizations of the Virasoro algebra in ℝ3. We describe all inequivalent realizations of the direct sum of the Witt algebras by Lie vector fields over ℝ3. This result enables complete description of all possible (1+1)-dimensional partial differential equations that admit infinite dimensional symmetry algebras isomorphic to the direct sum of Witt algebras. In this way we have constructed a number of new classes of nonlinear partial differential equations admitting infinite-dimensional Witt algebras. So new integrable models which admit infinite symmetry algebra are obtained.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
36 - 56
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1683964How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Qing Huang
AU  - Renat Zhdanov
PY  - 2021
DA  - 2021/01
TI  - Realizations of the Witt and Virasoro Algebras and Integrable Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 36
EP  - 56
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683964
DO  - https://doi.org/10.1080/14029251.2020.1683964
ID  - Huang2021
ER  -