Looped cotangent Virasoro algebra and non-linear integrable systems in dimension 2+1

Abstract

We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that leads to an integrable non-linear partial differential equation. This equation is an analogue of the Kadomtsev--Petviashvili (of type B) equation.

LaTeX, 21 pages

References in corpus (8)

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• Coadjoint orbits of the Virasoro algebra and the global Liouville equation
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• On dispersionless BKP hierarchy and its reductions
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• Representations of the Schrödinger-Virasoro algebras
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• Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems
• Recursion Operators and Nonlocal Symmetries for Integrable rmdKP and rdDym Equations
• Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms
• Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics
• Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras