Y. Murakami et M. Tajiri, RESONANT INTERACTION BETWEEN LINE SOLITON AND Y-PERIODIC SOLITON - SOLUTIONS TO THE KADOMTSEV-PETVIASHVILI EQUATION WITH POSITIVE DISPERSION, Journal of the Physical Society of Japan, 61(3), 1992, pp. 791-805
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.