We have numerically solved an extended version of the nonlinear Schrödinger equation, taking into account higher-order dispersion, the shock (self-steepening) term, and a term describing the Raman self-pumping of an ultrashort pulse. It is shown that the Raman effect is dominant on a femtosecond time scale and leads to the decay of higher-order solitons. For the case of the N = 2 soliton an intense pulse at a distinctly Stokes-shifted frequency is created. This pulse eventually shapes into a fundamental soliton, and its further evolution is governed by the combination of dispersion, self-phase modulation, and the soliton self-frequency shift.

© 1987 Optical Society of America

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