2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183295We 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 pagesMathematical PhysicsExactly Solvable and Integrable Systems17B68, 17B80, 35Q53text