An analytic approach to describe subpicosecond soliton dynamics is presented. It is argued that the modified
nonlinear Schrödinger (NLS) equation containing a nonlinearity dispersion term should be considered as a true
basic integrable model in the subpicosecond region, instead of a perturbed NLS equation. Unique features to
improve performance characteristics of optical systems in the subpicosecond region by matching properly soliton and medium parameters are illustrated by several examples, among which are dispersion-managed solitons and solitons in a nonlocal Kerr medium.
The modulational instability of continuous waves in nonlocal random focusing and defocusing media with saturable
nonlinearity is described. It is shown that nonlocality with a sign-definite Fourier image of the medium
response function reduces significantly the growth rate peak and bandwidth of instability caused by stochasticity.
Contrary, nonlocality can increase modulational instability growth rate for a response function with negative-sign bands.
The optical soliton train propagation is studied under the action of intra pulse Raman scattering (IRS). It is shown that IRS induces decay of the soliton train at het early stage of this propagation. As a method to suppress the adverse action of IRS, a train propagation in a composite medium with fast and slow relaxing cubic non-linearities is analyzed.
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