We demonstrate that the competing cubic-quintic nonlinearity induces propagating solitonlike dark(bright) solitons and double-kink solitons in the nonlinear Schrödinger equation with self-steepening and self-frequency shift. Parameter domains are delineated in which these optical solitons exist. Also, fractional-transform solitons are explored for this model. It is shown that the nonlinear chirp associated with each of these optical pulses is directly proportional to the intensity of the wave and saturates at some finite value as the retarded time approaches its asymptotic value. We further show that the amplitude of the chirping can be controlled by varying the self-steepening term and self-frequency shift.

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We demonstrate a different pulse compression technique based on exact solutions to the nonlinear Schrödinger-type equation interacting with a source, variable dispersion, variable Kerr nonlinearity, and variable gain or loss. We show that this model is appropriate for the pulse propagation in asymmetric twin-core fibers. The chirped pulses are compressed due to the nonlinearity as well as dispersion management as also due to the space dependence of the gain coefficient. We also obtain singular solitary wave solutions, pertaining to extreme increase of the amplitude due to self-focusing.

We analyse the structure of the exact, dark and bright soliton solutions of the driven nonlinear Schrödinger equation. A wide class of solutions, phase locked with the source, is identified for distinct parameter ranges. These contain periodic as well as localized solutions, which can be singular implying extreme increase in intensity. Conditions for obtaining non-propagating solutions are also found. A special case, where the scale of the soliton emerges as a free parameter, is obtained. We also study the highly restrictive structure of the localized solutions, when the phase and amplitude get coupled. Numerical solutions are obtained for this case, which reveals presence of periodic solutions. Stability analysis is also carried out through the Crank-Nicolson method.