Passage of a wave pulse through a zero-dispersion point in the nonlinear Schrodinger equation

We consider, numerically and analytically, a wave purse passing a point whe re the dispersion coefficient changes its sign from focusing to defocusing. Simulations demonstrate that, in the focusing region, the purse keeps a so liton-like shape until it is close to the zero-dispersion point, but then, after the passage of this point, the pulse decays into radiation if its ene rgy is below a certain threshold, or, in the opposite case, it quickly rear ranges itself into a new double-humped structure, with a minimum at the cen ter, twin maxima propagating away from the center, and decaying tails. In t he focusing region, the pulse distortion is correctly described by the well -known adiabatic approximation, provided that it has sufficient energy. In the defocusing region, we find analytically an exact reduction of the under lying nonlinear-Schrodinger equation with a linearly varying dispersion coe fficient to an ordinary differential equation. Comparison with the numerica l simulations suggests that the inner region of the double-humped structure is accurately represented by solutions of this ordinary differential equat ion. The separation between the maxima is thus predicted to grow nearly lin early with the propagation distance, which accords with the numerical resul ts. The structure found in this work may be readily observed experimentally in dispersion-decreasing nonlinear optical fibers. (C) 1999 Elsevier Scien ce B.V. All rights reserved.