RESONANT INTERACTION BETWEEN LINE SOLITON AND Y-PERIODIC SOLITON - SOLUTIONS TO THE KADOMTSEV-PETVIASHVILI EQUATION WITH POSITIVE DISPERSION

The exact solutions to the Kadomstev-Petviashvili equation with positi ve dispersion are analysed to study the interaction between line solit on and y-periodic soliton (i.e. the array of the localized structures in the y direction, which propagates in the x direction). The interact ions are classified into several types according to the phase shifts d ue to collision. There are two types of singular interactions: one is the resonant interaction that generates one line soliton while the oth er is the extremely repulsive or long-range interaction where two soli tons interchange each other infinitely apart. Both interactions are as sociated with the parametric points on the boundary between the region s, where the transverse phase shift can occur and that for no transver se phase shift. Detail behaviors of interactions are illustrated graph ically and the differences from the singular interactions in other cas es are described.