Solitons and Similaritons of a Generalized Nonlinear Schrödinger Equation with Variable Coefficients in a Power-Law Medium

We obtain the similarity transformation and construct analytical soliton and similariton solutions for the generalized nonlinear Schrödinger equation with varying dispersion, power-law nonlinearity, and attenuation, which could describe the propagation of optical pulse in inhomogeneous fiber systems. Based on these solutions, we discuss dynamical behaviours of the chirped similariton and the chirp-free soliton in the dispersion decreasing fiber and the periodic distributed system. In the first soliton control system, we can control the compression and stretching by modulating the dispersion parameter σ. The pulse is compressed for parameter σ > 0, while the pulse is stretched for parameter σ < 0. In the second soliton control system, the snake-like propagation behaviour disappears little by little and the period of waves gradually decreases with the increasing of the index of the power-law nonlinearity. Compared with chirped similaritons, chirp-free solitons remain with the certain amplitude and width in two systems.