We study soliton solutions of the Kadomtsev-Petviashvili II equation $(-4u_t+6u{u}_x+3u_{xxx}{)}_x+u_{yy}=0$ 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 $y\to \infty$ coincide with those of the $N$ asymptotic line solitons as $y\to -\infty$. 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.

• Received 3 April 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.064103