Solitary chirp pulses and soliton control for variable coefficients cubic–quintic nonlinear Schrödinger equation in nonuniform management system

Abstract This study investigates the variable coefficient cubic–quintic nonlinear Schrödinger equation, which models the propagation of ultrashort femtosecond pulses in optical fibers and three-body recombination losses in Bose–Einstein condensates. Using a mapping technique combined with an extended chirp wave transformation, 20 chirp wave solutions were derived, including bright and dark solitons, kink waves, periodic and singular waves. These solutions encompass previously reported results and introduce novel ones. Three-dimensional plots illustrate the soliton and kink chirp wave solutions for both constant and exponentially varying group velocity dispersion (GVD) and Raman effect parameters. Analysis reveals that the sign of the Raman effect parameter influences the soliton type, yielding bright solitons for positive values and dark solitons for negative values. Furthermore, both GVD and Raman effect significantly impact the wave shape, inducing oscillations in the case of exponentially distributed fiber. The stability of the soliton wave solution is also analyzed. These diverse wave profiles have potential applications in nonlinear optics and plasma physics.