A first principles derivation is given of the evolution equation for nonlinear pulse propagation in an optical fibre. It avoids many of the difficulties encountered in some other theories and emphasises that waveguide effects can be included in a natural and logical manner. It is preceded by a brief review of the principal features of solitons in optical guides, and a critical discussion is given of previous theoretical descriptions of them. The numerical results reported here include an investigation of the competitive roles of waveguide and material dispersion and some examples of the behaviour of solitary wave solutions of the nonlinear Schrodinger equation.