This paper will present the nonlinearity and dispersion effects
involved in propagation of optical solitons, which can be understood by
using a numerical routine to solve the nonlinear Schrödinger equation
(NLSE). Here, Mathematica v5© (Wolfram,
2003) is used to explore in depth several features of optical
solitons formation and propagation. These numerical routines were
implemented through the use of Mathematica v5© and the results give a
very clear idea of this interesting and important practical phenomenon. It
is hoped that this work will open up an important new approach to the
cause, effect, and correction of interference from secondary radiation
found in the uses of soliton waves in lasers and in optical fiber
telecommunication. It is believed that these results will be of
considerable use in any work or research in this field and in
self-focusing properties of the soliton (Osman et al., 2004a, 2004b; Hora, 1991).
In a previous paper on this topic (Beech & Osman,
2004), it was shown that solitons of NLSE radiate. This paper goes
on from there to show that these radiations only occur in solitons derived
from cubic, or odd-numbered higher orders of NLSE, and that there are no
such radiations from solitons of quadratic, or even-numbered higher order
of NLSE. It is anticipated that this will stimulate research into
practical means to control or eliminate such radiations.
Stable Pulse Solutions for the Nonlinear Schrödinger Equation with Higher Order Dispersion Management
