Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers (Q1381161)

The authors study, using the so-called semiclassical approximation, evolution of an initial pulse in a nearly rectangular form, in the exactly integrable nonlinear Schrödinger equation with self-defocussing. Earlier, it was demonstrated that, in the case when the initial pulse is exactly rectangular, its gradual decay does not lead (in the approximation described by the Riemann invariants) to formation of shock waves of the phase. The present authors demonstrate a structural instability of this result: any smoothing of the rectangular pulse produces the shock waves. After formation of the shocks, the description based on the Riemann invariants becomes inapplicable, but it is known that the shock waves give rise to oscillations developing in the wave generated by the initial pulse.