2014/07/21 by Renat Zhdanov, Qing Huang, Zhdanov, Renat +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1407.5387
openalex publication_date 2014/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain exhaustive classification of inequivalent realizations of the Witt and Virasoro algebras by Lie vector fields of differential operators in the space ℝ3. Using this classification we describe all inequivalent realizations of the direct sum of the Witt algebras in ℝ3. These results enable constructing all possible (1+1)-dimensional classically integrable equations that admit infinite dimensional symmetry algebra isomorphic to the Witt or the direct sum of Witt algebras. In this way the new classically integrable nonlinear PDE in one spatial dimension has been obtained. In addition, we construct a number of new nonlinear (1+1)-dimensional PDEs admitting infinite symmetries.