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

Valentin Ovsienko (1) , Claude Roger (1)

1 ICJ - Institut Camille Jordan

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.

Mots clés: Virasoro algebra; Euler equation; BKP equation

Domaines: Physique mathématique [math-ph]; Systèmes Solubles et Intégrables [nlin.SI]

Valentin Ovsienko, Claude Roger. Looped cotangent Virasoro algebra and non-linear integrable systems in dimension $2+1$. 2006. ⟨hal-00019154v2⟩