In this talk, we report our recent results on the dispersive revival and fractalization phenomena for two-dimensional linear dispersive equations over a bounded domain on the plane subject to periodic boundary conditions. In particular, we study the periodic initial-boundary value problem for the linear Kadomtsev-Petviashvili equation subject to step-function initial data on a square, and analyze the manifestation of the revival phenomenon for the corresponding solution at rational times.  We show that the solution will take on different qualitative behavior in x-direction and y-direction.