Breathers are oscillating localised wave (modes) in many different physical systems. They are new research direction in nonlinear physics, where the physics has not be well-revealed. Breathers are known in optics, hydrodynamics, Bose-Einstein condensates, micromechanical arrays, and in the cavity optomechanics. They provide a basis for more complicated formations—nonlinear superpositions of breathers that appear in many nonlinear phenomena of physical importance such as rogue wave events, breather

molecules, chess-board-like patterns, turbulence, higher-order modulation instability, and the MI where small periodic modulation is additionally localised in transverse direction, i.e., the super-regular breathers.