  We discover new type of interference patterns generated in the focusing
nonlinear Schr\"odinger equation (NLSE) with localised periodic initial
conditions. At special conditions, found in the present work, these patterns
exhibit novel chess-board-like spatio-temporal structures which can be observed
as the outcome of collision of two breathers. The infinitely extended
chess-board-like patterns correspond to the continuous spectrum bands of the
NLSE theory. More complicated patterns can be observed when the initial
condition contains several localised periodic swells. These patterns can be
observed in a variety of physical situations ranging from optics and
hydrodynamics to Bose-Einstein condensates and plasma.
