Dynamics and trajectory of nonautonomous rogue wave in a graded-index planar waveguide with oscillating refractive index

We study rogue waves in a graded-index planar waveguide with oscillating refractive index. We find that an additional refractive index can be used to manipulate the trajectory of the rogue wave without changing its shape evolution characters. The density distribution profile of rogue wave with the highest peak can be kept well through manipulating the graded-index term and nonlinear coefficient. Furthermore, the trajectories of these nonautonomous rogue waves still look like an “X” shape. These results provide possibilities to manipulate rogue wave in nonautonomous nonlinear systems.