Four-wave mixing in wavelength-division-multiplexed soliton systems: Ideal fibers

Analytic expressions for four-wave-mixing terms in an ideal, lossless wavelength-division-multiplexed soliton system are derived with an asymptotic expansion of the N-soliton solution of the nonlinear Schrödinger equation. The four-wave contributions are shown to grow from a vanishing background and then to decay. Their importance becomes evident in real, nonideal fibers, where they grow by an order of magnitude and equilibrate to a stable value as an effect of periodic amplification.