Rogue waves management by external potentials

We study the effect of time-dependent linear and quadratic potentials on the profile and dynamics of rogue waves represented by a Peregrine soliton. The Akhmediev breather, Ma breather, bright soliton, Peregrine soliton, and constant wave (CW) are all obtained by changing the value of one parameter in the general solution corresponding to the amplitude of the input CW. The corresponding solutions for the case with linear and quadratic potentials were derived by the similarity transformation method. While the peak height and width of the rogue wave turn out to be insensitive to the linear potential, the trajectory of its center-of-mass can be manipulated with an arbitrary time-dependent slope of the linear potential. With a quadratic potential, the peak height and width of the rogue wave can be arbitrarily manipulated to result, for a special case, in a very intense pulse.