The Akhmediev breather is an exact solution of the nonlinear Schrödinger equation (NLS) iψ_t + ½ψ_xx + |ψ|²ψ = 0, describing a modulation instability that grows on a uniform background and peaks at one location in time. At the limit of infinite modulation period, it becomes the Peregrine soliton — the prototypical rogue wave with amplitude 3× the background.