Gino Biondini
Ohio State University
Abstract:
We consider a family of solutions of the Kadomtsev-Petviashvili (KPII) equation (-4u_t+u_{xxx}+6uu_x)_x + 3u_{yy} = 0 which also satisfy the Toda lattice hierarchy. We show that all of these solutions are of resonant type, consisting of an arbitrary number of line solitons in both aymptotics: an arbitrary number M of incoming solitons for y\to-\infty interacts to form an arbitrary number N of outgoing solitons for y\to\infty. We characterize the number of solitons, as well as their amplitudes and velocities, in terms of the parameters of the solution. We also characterize the interaction patterns, and show that the resonant interaction creates a web-like structure with (M-1)(N-1) holes. Finally, we briefly discuss the practical implications of these results.