Realizations of the Witt and Virasoro Algebras and Integrable Equations

DOI

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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TY  - JOUR
AU  - Qing Huang
AU  - Renat Zhdanov
PY  - 2019
DA  - 2019/10/25
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  - 10.1080/14029251.2020.1683964
ID  - Huang2019
ER  -