Time evolution of perturbed solitons of modified Kadomtsev-Petviashvili equations

We solve the (2+1)-dimensional Schamel-Kadomtsev- Petviashvili equations with negative and positive dispersion numerically with one or two perturbed plane solitons as initial conditions. In the negative dispersion case, the plane soliton is stable and retains its identity. For the equation with positive dispersion, the plane solitons decay into two- dimensional lump solitons. We show that in contrast to one- dimensional solitons, collisions between two lump solitons are far from elastic. We also demonstrate that the solitons emerging from the collision can be very sensitive to the alignment of the solitons prior to collision.