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A perturbative approach is used to obtain small-amplitude solitary structures for an extended nonlinear Schrödinger equation. These structures have the form of dark and anti-dark solitary wave solutions, closely connected with the Korteweg - deVries solitons. The solutions found are valid in wavelength regions, such as those applicable in the anomalous dispersion regime, which are not accessible by the conventional nonlinear Schrödinger equation. The dynamics of the derived structures in the presence of the Raman effect is also studied by means of a Korteweg - deVries - Burgers equation. The obtained results are applied to the problem of propagation of femtosecond duration pulses in nonlinear optical fibres.
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D. J. Frantzeskakis (1996) studied this question.
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