Engineering of chirp localized waves in optical media with positive group velocity dispersion

In this work, we combine the phase engineering method with the generalized perturbation (n,N−n)-fold Darboux transformation to study the generation of mixed localized chirped pulses in optical fibers with positive group velocity dispersion whose dynamics are described by a cubic–quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift. Analytical localized wave solutions with nonlinear chirps of the model equation are presented in terms of fractional forms of determinants. The wave structures of these localized wave solutions of the model equation are discussed in detail for different parameters, which display abundant interesting wave structures such as interactions between multi-soliton and breathers, and may be useful to study the physical mechanism of mixed localized chirped waves in optics media with positive group velocity dispersion. Parameters of the group velocity dispersion and cubic nonlinearity are found to be useful for controlling the mixed localized waves in the optical media under consideration. We show that the nonlinear chirp associated with each of these optical mixed localized pulses is directly proportional to the intensity of the wave and can be controlled by the parameter of the group velocity dispersion and those of self-steepening term and self-frequency shift. Also, we show that to each of the optical mixed localized pulses corresponds a variety of frequency chirps whose behaviors depend on parameters of the self-steepening term and self-frequency shift. Finally, our analytical predictions are validated through direct numerical simulations of the model equation.