Are rogue waves robust against perturbations?

We study the effect of various perturbations on the fundamental rational solution of the nonlinear Schrödinger equation (NLSE). This solution describes generic nonlinear wave phenomena in the deep ocean, including the notorious rogue waves. It also describes light pulses in optical fibres. We find that the solution can survive at least three types of perturbations that are often used in the physics of nonlinear waves. We show that the rational solution remains rational and localized in each direction, thus representing a modified rogue wave.