Controllable Rogue Waves in the Generalized Nonlinear Schrödinger Equations

We obtain the rogue waves with a controllable center in the generalized nonlinear Schrödinger equation by using a direct method. The position of these solutions can be controlled by varying different center parameters. We study the effects of different parameters on rogue waves and hence find that the nonlinearity parameter is responsible for the width of rogue waves. With the increase of the nonlinearity parameter, the rogue wave becomes wider. What is more, the negative nonlinearity parameter can yield some singular rogue waves.