Calculation of timing and amplitude jitter in a dispersion-managed Korteweg–de Vries system

Propagation of weakly nonlinear long waves in a periodically inhomogeneous medium is considered in the framework of the variable-coefficients Korteweg–de Vries equation. Explicit formulas with which to compute timing and amplitude jitter caused by nonlinear interactions between adjacent solitary waves in a random data sequence are obtained. The results show that the timing jitter depends on the quadratic growth of the propagation distance, whereas the amplitude jitter exhibits a simple linear dependence in the considered periodically varying dispersion-managed Korteweg–de Vries system. By contrast, both timing and amplitude jitter are found to be in the form of a linear growth to distance in a transmission system with strong periodic dispersion management.