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Nonautonomous Dark Solitons and Rogue Waves in a Graded-Index Grating Waveguide

We analytically present a family of nonautonomous dark solitons and rogue waves in a planar graded-index grating waveguide with an additional long-period grating. The dark solitons whose dynamics described by the explicit expressions such as the valley, background and wave central position are investigated. We find that dark soliton's depth and the long-period grating have effects on soliton's wave central position; the gain or loss term affects directly both the background and valley of the soliton. For rogue waves, it is reported that one can modulate the distribution of the light intensity by adjusting the parameters of the long-period grating. Additionally, more rogue waves with different evolution behaviors in this special waveguide are demonstrated clearly.