Chirped femtosecond solitons and double-kink solitons in the cubic-quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift

We demonstrate that the competing cubic-quintic nonlinearity induces propagating solitonlike dark(bright) solitons and double-kink solitons in the nonlinear Schr\"odinger 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.