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 study the nature of the interactions between y-periodic soliton and line soliton and between y-periodic soliton and algebraic soliton. The interactions are classified into several types according to the phase shifts due to collisions. There are two types of singular interactions: one is the resonant interaction where two solitons interact so as to make one soliton and the other is the extremely long-range interaction where two solitons interchange each other infinitely apart. Detail behaviors of interactions are illustrated graphically.