Qualitative Dynamics of Modulated Soliton Pulse Trains

Abstract

The recent advances in the technology of passive optical amplification have brought closer the realisation of optical fibre communication systems using soliton pulses which are not limited by dispersion. This in turn creates a new generation of theoretical problems concerned with the evolution of information-bearing pulse trains along a nonlinear channel. Previously, these theoretical models have been constructed primarily on the basis of the behaviour of isolated 1 - or 2-soliton phenomena, as deduced by perturbation theory carried out on the Inverse Scattering Theory (IST) for the exactly-integrable Nonlinear Schrodinger Equation (NLSE) [1-4] or by direct numerical solution of the NLSE [5,6]. However, there are many circumstances in which the behaviour of a small number of isolated solitons may not properly represent the behaviour of a very long pulse train with neighbouring pulses coupled by a weak nonlinear intersoliton interaction; for example, two isolated solitons in the repulsive phase of the intersoliton interaction will diverge apart indefinitely, but this cannot happen when those two pulses form part of a long train of pulses, since the diverging pulses must eventually meet and interact with other pulses in the same train. Although the IST method is extremely useful for predicting the evolution of initial conditions consisting of a small number of solitons in the absence of an IST continuum, the presence of a large number of solitons or IST continuum in the initial conditions renders the method intractable. Even the simplest case of an infinitely long pulse train of periodically repeated identical solitons involves much more difficult analytical techniques than the conventional IST method and the true physical case of a modulated pulse train containing an infinite number of solitons is not tractable by any known analytical method, despite preserving the integrability of the NLSE.