PAINLEVE ANALYSIS AND REDUCIBILITY TO THE CANONICAL FORM FOR THE GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION

The most general Kadomtsev-Petviashvili (KP) type equation, [u(t) + a(t,x,y)u + b(t,x,y)u(x) + c(t,x,y)uu(x) + d(t,x,y)u(xxx)]x + k(t,x,y)u(yy) = e(t,x,y), is studied and the conditions for the coefficients, in order that it owns complete integrability, are determined via a Painleve test. Finally, it is proved that the above conditions are the same as those requested for reducing the equation to the canonical form via suitable transformations.