Gray optical dips in the subpicosecond regime.

Narrow optical dip solutions are investigated when, besides self-phase modulation and group velocity dispersion, also third-order dispersion, nonlinear dispersion, and stimulated Raman scattering are taken into account. By using the inverse scattering transform for the higher-order optical nonlinear Schrödinger (HNLS) equation under Hirota parameter conditions, the dark N-soliton solution is constructed. The explicit forms of the one- and two-soliton solutions are investigated in detail. The results show an interesting property of the gray two-soliton solution. Two gray dips do not interact provided their modulation depths are appropriately chosen. In addition, when generalizing the HNLS equation (to regions beyond the Hirota parameter conditions), it can be shown that also quite stable generalized two-dip solitary wave solutions exist. The latter, although not belonging to integrable systems, approximately preserve most of the interesting properties detected for the integrable Hirota equation.