New chirped gray and kink self–similar waves in presence of quintic nonlinearity and self–steepening effect

•A generalized derivative nonlinear Schrodinger equation with varying coefficients is studied.•self-similar structures take the shape of gray and kink pulses are reported.•The corresponding frequency chirp is obtained. We demonstrate new types of chirped self-similar waves for a generalized derivative nonlinear Schrödinger equation with varying dispersion, self–steepening effect, cubic–quintic nonlinearity, and gain or loss. The equation arises in modeling femtosecond light propagation in an optical fiber with spatial parameter variations. The newly found self-similar structures take the shape of gray and kink pulses. It is observed that the frequency chirp accompanying these self-similar pulses depends crucially on the intensity of the wave and its amplitude can be effectively governed by adjusting the self-steepening parameter. The dynamical behaviors of the chirped self-similar gray and kink waves are analyzed in a periodic distributed amplification system. The acquired self-similar structures display rich dynamical evolutions that are important in practical applications.