We present an approximate theory of nonlinear pulse propagation in homogeneous and inhomogeneous waveguides. Our analysis takes account of physical effects arising from transverse confinement, dispersion, and nonlinearity. We find that both bright and dark solitons may be supported by typical waveguides under a variety of conditions. Moreover, it is possible to achieve a condition of “zero dispersion,” in which a soliton of arbitrarily small amplitude may be propagated, independent of pulsewidth. In the presence of weak longitudinal inhomogeneity, we find that solitions continue to propagate without a change of shape, but that their group velocity becomes time dependent.
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