On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy

We describe the interaction pattern in the x-y plane for a family of soliton solutions of the Kadomtsev-Petviashvili (KP) equation, (-4u _t, + u_xxx + 6uu_x)_x + 3u _yy = 0. The solutions considered also satisfy the finite Toda lattice hierarchy. We determine completely their asymptotic patterns for y → ±∞, and we show that all the solutions (except the 1-soliton solution) are of resonant type, consisting of arbitrary numbers of line solitons in both asymptotics; that is, arbitrary N_-L incoming solitons for y → -∞ interact to form arbitrary N₊ outgoing solitons for y → ∞. We also discuss the interaction process of those solitons, and show that the resonant interaction creates a web-like structure having (N_- - 1)(N₊ - 1) holes.