Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification

In this paper, we show that there can be four wave mixing between three solitons having different, but equally spaced, frequencies. While this does not happen with solitons in a uniform lossless fiber, we show that in a transmission line with loss and periodically placed amplifiers, it can happen. The spatial periodicity of the transmission line serves to phase match the four wave mixing of the three solitons. This results in permanent frequency shifts for two of the three solitons and energy exchanges between all three solitons