Phase jitter in single-channel soliton systems with constant dispersion

The phase jitter of optical solitons in single-channel communication systems with constant dispersion and distributed amplification is studied in detail. The variational method is used to derive equations that model phase jitter caused by amplifier noise. These equations are solved analytically. Simple formulas are obtained for the phase variance of an ensemble of solitons, which together cover the entire range of practical transmission distances. These formulas are validated for parameters of current interest by numerical solutions of the nonlinear Schroedinger equation.