On the calculation of the timing shifts in the variable-coefficient Korteweg-de Vries equation

The variable-coefficient Korteweg-de Vries equation that governs the dynamics of weakly nonlinear long waves in a periodically variable dispersion management media is considered. For general bit patterns, an analytic expression describing the evolution of the timing shift produced by nonlinear interactions between neighboring solitons is derived. The general result with a Gaussian like solitary wave profile for a special case of negligible average dispersion is tested. By considering a piecewise-constant map, we found that the timing shift is reduced substantially in the dispersion-managed Korteweg-de Vries system.