Numerical simulations show that higher order KdV equation under certain conditions has a self-focusing singularity, which means that the solution of the equation blows up in finite time. In this paper, two numerical schemes: the split-step Fourier transform and the pseudospectral methods are...

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...