Chessboard-like spatio-temporal interference patterns and their excitation

We discover a new type of interference pattern generated in the focusing nonlinear Schrödinger equation (NLSE) with localized initial conditions consisting of a continuous wave with cosinoidal modulation that varies in amplitude. Namely, the amplitude decays to the continuous-wave amplitude at each side of the perturbation. For short, we can call it localized cosinoidal perturbation (LCP). Under special conditions, found in the present work, these patterns exhibit novel chessboard-like spatio-temporal structures that can be observed as the outcome of the collision of two breathers. The infinitely extended chessboard-like patterns correspond to the continuous finite-band spectrum of the NLSE theory. More complicated patterns can be observed when the initial condition contains several LCPs separated in the transverse direction. These patterns can be observed in a variety of physical situations ranging from optics and hydrodynamics to Bose-Einstein condensates and plasma.