Abstract
A systematic method which is based on the classical Lie group reduction is used to find the novel exact solution of the nonlinear Schrodinger equation (NLS) with distributed dispersion, nonlinearity and gain or loss. We study the transformations between the standard NLS equation and the NLS equations with distributed dispersion, nonlinearity and gain or loss. Appropriate solitary wave solutions can be applied to discuss soliton propagation in optical fibres, and the amplification and compression of pulses in optical fibre amplifiers.
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