Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation

The interaction of two lump solitons described by the Kadomtsev-Petviashvili I(KPI) equation is analyzed using both exact and numerical methods. The numerical method is based on a third order Runge-Kutta method, and a Crank- Nicholson scheme. The main characteristic of a direct interaction when the two lumps are initially aligned along the x-axis, is that they may separate in the y-direction, but then come back to the xaxis after collision; the dependence of the maximum separation in the y-direction on the relative velocity difference is described. Two lumps may also experience an abrupt phase change in the case of an oblique interaction