Numerical simulation of the semi-classical limit of the focusing nonlinear Schrodinger equation

We present a series of careful numerical experiments on the semi-classical limit of the focusing nonlinear Schrodinger equation. We observe the emergence of an ordered train of solitons, which was originally predicted by one of the authors based on a numerical and analytical study of the Zakharov-Shabat eigenvalue problem. The velocity and amplitude of the solitons in the train are in extremely good agreement with the predictions of the previous work. We also observe a difference in behavior between analytic and non-analytic initial data which suggests that, at least for certain initial data, the elliptic modulation equations are correct. (C) 1999 Published by Elsevier Science B.V.