The pp-wave metrics describe various types of gravitational waves and are given by:
ds2 = H(u,x,y)du2 + 2dudv + dx2 + dy2
where H is a function of at most 3 variables. An important class of pp-waves are the plane gravitational waves and are obtained by choosing
H(u,x,y) = a(u)x2 + b(u)y2 + c(u)xy