Resonant interactions of Y-periodic soliton with line soliton and algebraic soliton: Solutions to the Davey-Stewartson I equation

The exact solutions to the Davey-Stewartson I equation are analyzed to stud y the nature of the interactions between y-periodic soliton and line solito n and between y-periodic soliton and algebraic soliton. The interactions ar e classified into several types according to the phase shifts due to collis ions. There are two types of singular interactions: one is the resonant int eraction where two solitons interact so as to make one soliton and the othe r is the extremely long-range interaction where two solitons interchange ea ch other infinitely apart. Detail behaviors of interactions are illustrated graphically.