Line soliton interactions of the kadomtsev-petviashvili equation

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4ut+6uux+3uxxx)x+uyy=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y→ coincide with those of the N asymptotic line solitons as y→. We also show that the (2N-1)!! types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.