Stability and Quasi-Equidistant Propagation of NLS Soliton Trains

Using the complex Toda chain (CTC) as a model for the propagation of the N-soliton pulse trains of the nonlinear Schroedinger (NLS) equation, we can predict the stability and the asymptotic behavior of these trains. We show that the following asymptotic regimes are stable: (1) asymptotically free propagation of all N solitons; (2) bound state regime where the N solitons move quasi-equidistantly; and (3) various different combinations of (1) and (2). On the example of N = 3 we show how the CTC model can be used to determine analytically the set of initial soliton parameters corresponding to regime (2). We compare these analytical results against the corresponding numerical solutions of the NLS and find excellent agreement in most cases. We concentrate on the quasi-equidistant propagation of all N solitons because it is of importance for optical fiber soliton communication. We check numerically that such propagation takes place for N = 2 to S. Finally we propose realistic configurations for the sets of the amplitudes, for which the trains show quasi-equidistant behavior to very large run lengths.