| Summary: | Solitons have been proposed as information carriers in next generation fibre optic networks. As the stable waveform in nonlinear optical fibres, solitons are resistant to a wide variety of perturbations from fibre effects, optical devices and other solitons. While they are a particularly robust waveform, solitons must be periodically amplified in order to compensate for fibre loss. This amplification causes random fluctuations in the soliton's position, thus limiting the potential data transfer rates in soliton-based fibre optic networks. As a result fibre optic networks utilising solitons will also have to be filtered in order to remove harmful background radiation. A variety of other devices may be necessary for soliton control or modification. One such device is a fibre compressor which is a section of dispersion decreasing fibre. When passed through a fibre compressor, a train of solitons will decrease in width and show a proportional increase in amplitude. This allows a higher data transfer rate. It is of interest to determine the evolutionary behaviour of solitons in fibre optic networks containing the above mentioned devices and fibre properties. The constituent equation modelling pulse evolution in a nonlinear optical fibre is the nonlinear Schrödinger (NLS) equation. The NLS equation possesses an exact inverse scattering solution. However the evolution to the steady state from an initial pulse is governed by an integral equation and so is difficult to determine. It is this evolutionary behaviour which is of interest. In addition, modelling the above mentioned optical devices and fibre effects requires adding perturbing terms to the NLS equation. These perturbed NLS equations do not possess inverse scattering solutions and so analytical solutions do not exist. Both of these factors lead to the use of approximate and computational techniques to analyse evolutionary pulse behaviour of perturbed NLS equations.
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