The manipulation of optical rogue waves for the nonautonomous nonlinear Schrodinger equation

We obtain analytical solutions that describe self-similar rogue waves for the (1+1)-dimensional nonautonomous nonlinear Schrodinger equation with a linear potential. The explicit functions that describe the evolution of the width, peak, and phase are found exactly, from which it can be seen that the gain-loss parameter has no effect on the motion of rogue waves' phases or their widths, and affects only the evolution of their peaks. We also find that the manipulation of rogue waves can be realized by modulating the values of the maximum accumulated time, T-m, and the accumulated time, T-0, with the maximum amplitude of the rogue waves. The controllability for the type of excitation, such as sustainment, recurrence, and annihilation for rogue waves and the transverse position of excitation is exhibited.