The management and containment of self-similar rogue waves in the inhomogeneous nonlinear Schrödinger equation

We present, analytically, self-similar rogue wave solutions (rational solutions) of the inhomogeneous nonlinear Schrödinger equation (NLSE) via a similarity transformation connected with the standard NLSE. Then we discuss the propagation behaviors of controllable rogue waves under dispersion and nonlinearity management. In an exponentially dispersion-decreasing fiber, the postponement, annihilation and sustainment of self-similar rogue waves are modulated by the exponential parameter σσ. Finally, we investigate the nonlinear tunneling effect for self-similar rogue waves. Results show that rogue waves can tunnel through the nonlinear barrier or well with increasing, unchanged or decreasing amplitudes via the modulation of the ratio of the amplitudes of rogue waves to the barrier or well height.

► Self-similar rogue wave solutions of the inhomogeneous NLSE are obtained.
► Postponement, annihilation and sustainment of self-similar rogue waves are discussed.
► Nonlinear tunneling effects for self-similar rogue waves are investigated.