Rogue wave is a kind of surface gravity waves with much larger wave heights than expected in normal sea state. Since this extreme sea event always occurred in the areas with strong currents, the wave-current interaction was considered to be one of the physical mechanics of the formation of the rogue wave. Some breather type solutions of the NLS equation have been considered as prototypes of rogue waves in ocean which usually appears from smooth initial condition only with a certain disturbance. In this paper, we have numerically studied evolutionary process of the Peregrine breather rogue wave based on the current modified fourth order nonlinear Schrödinger equation (the CmNLS equation). During the generation and evolution of the Peregrine breather rogue wave, the effects of the steady current was investigated by comparing with the results without current. The differences of the focusing position/time were observed due to the current influence.

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