Ultrashort self-similar solutions of the cubic-quintic nonlinear Schrodinger equation with distributed coefficients in the inhomogeneous fiber

By means of the similarity transformation, we obtain exact self-similar solutions (similaritons) of the generalized cubic-quintic (CQ) nonlinear Schrodinger equation with spatially inhomogeneous group velocity dispersion, CQ nonlinearity and amplification or attenuation. Exact balance conditions between the dispersion, nonlinearity and the gain/loss have been obtained. As an example, we investigate their propagation dynamics in the dispersion decreasing fiber (DDF). Considering the fluctuation of the fiber parameter in real application, the exact balance conditions do not satisfy, and so we perform direct numerical analysis with initial 10% white noise for the bright similariton in both the DDF and the periodic distributed amplification system. Numerical calculations indicate stable propagation of the bright similariton over tens of dispersion lengths. These ultrashort self-similar optical waves are potentially useful for all-optical data-processing schemes and the design of beam compressors and amplifiers.