The cylindrical Kadomtsev-Petviashvili equation; its Kac-Moody-Virasoro algebra and relation to KP equation

Abstract We show that a class of integrable nonlinear differential equations in 2+1 dimensions, including the physically important cylindrical Kadomtsev-Petviashvili equation, has a symmetry algebra with a specific Kac-Moody-Virasoro structure. The isomorphism between this algebra and the symmetry algebra of the KP equation, is used to transform the entire class into the KP equation, by a Lie point transformation. This transformation makes it possible to solve completely the Cauchy problem for the cylindrical KP equation.