Realizations of the Witt and Virasoro Algebras and Integrable Equations
- https://doi.org/10.1080/14029251.2020.1683964How to use a DOI?
- Witt algebra, Virasoro algebra, Lie vector field, equivalence transformation, integrable equation
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.
- © 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 -