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 analysed 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 x-axis 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. (C) 2004 Elsevier B.V. All rights reserved.