Resonance interaction of breathers in the Manakov system

By means of the dressing technique, we build multipole solutions of the focusing Manakov system under a constant background. These solutions become degenerate when the poles of the dressing function merge. We find that with a special choice of the integration constants, such solutions describe the fusion or decay of the pulsing solitons—breathers—and their wave numbers and frequencies satisfy the typical resonance condition. We investigate the different cases of such resonance interactions.