Nonautonomous spatiotemporal localized structures in the inhomogeneous optical fibers: Interaction and control

We develop a systematic way to find the similarity transformation and investigate nonautonomous optical similariton dynamics for (n + 1)-dimensional nonlinear Schrödinger equation in the inhomogeneous optical fibers. A condition between the parameters of the mediums, which hints a exact balance between the dispersion/diffraction, nonlinearity and the gain/loss, has been obtained. Under this condition the optical similariton transmission in the dispersion-decreasing fibers (DDF) can be exactly controlled by proper dispersion management. Moreover, novel propagation dynamics of bright and dark similaritons on the background waves and optical rogue waves (rogons) in DDF are investigated too.

Research highlights
► The similarity transformation of (n + 1)-dimensional inhomogeneous NLSE are found.
► From transformation, analytical self-similar waves and rogue waves are obtained.
► Dynamical behaviors of self-similar waves in DDF are discussed.
► The propagation and control of spatiotemporal self-similar waves are presented.