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Optical rogue waves and its variants have been studied quite extensively inthe context of optical fiber in recent years. It has been realized thatdispersion management in optical fiber is experimentally much more feasiblecompared to its nonlinear counterpart. In this work, we report Kuznetsov-Ma(KM)-like breathers from the first three orders of rational solutions of thenonlinear Schr\"{o}dinger equation with periodic modulation of the dispersioncoefficient along the fiber axis. The breather dynamics are then controlled byproper choice of modulating parameters. Additionally, the evolution of newone-peak and two-peak breather-like solutions has been displayed correspondingto the second-order rational solution. Direct numerical simulations based onmodulational instability has also been executed which agree well with theanalytical results, thereby making the proposed system more feasible forexperimental realization.

Dispersion Managed Generation of Peregrine Solitons and Kuznetsov-Ma Breather in an Optical Fiber