On realizations of the Virasoro algebra
Renat Zhdanov, Qing Huang
TL;DR
This paper classifies all possible realizations of the Virasoro algebra as Lie vector fields in three dimensions and uses this to find new nonlinear PDEs with infinite-dimensional symmetries.
Contribution
It provides a complete classification of Virasoro algebra realizations and constructs new nonlinear PDEs with rich symmetry structures.
Findings
Complete classification of Virasoro algebra realizations.
Construction of new nonlinear PDEs with infinite-dimensional symmetries.
Identification of applications in symmetry analysis of differential equations.
Abstract
We obtain complete classification of in-equivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers. As an application we construct new classes of nonlinear second-order partial differential equations possessing infinite-dimensional Lie symmetries.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Algebraic structures and combinatorial models