Chirped periodic waves and solitary waves for a generalized derivative resonant nonlinear Schrödinger equation with cubic–quintic nonlinearity

We investigate the self-similar propagation of one-dimensional optical waves through optical fibers exhibiting self-steepening, dispersion, cubic–quintic nonlinearity and resonant. A generalized derivative resonant nonlinear Schrödinger model with cubic–quintic nonlinear medium governing the evolution of optical pulses is studied, and analytical solutions of the model are extracted together with different material parameters. A full range of solitons and periodic wave solutions leading with nonlinear chirp is obtained. In long wave limit, chirped localized waves including solitary waves are obtained in a continuous wave background. The model exhibiting distributed parameters in inhomogeneous medium is also examined via similarity transformation method. Analytical self-similar chirped solitary beams are identified, which have quadratic phase variation in time suggesting linearity of associated frequency of chirping. The chirping ensures interesting features, and it can relevantly control the self-similar structure and its dynamical behavior. The applicability is demonstrated by choosing a periodic-distributed fiber amplification system.