Propagation dynamics of nonautonomous solitons in a temporally modulated cubic–quintic–septimal nonlinear medium

We investigate the behavior of optical solitons within a nonlinear medium characterized by temporally varying second-order dispersion, cubic–quintic–septimal nonlinearities, and linear gain or loss. Our analysis yields analytical solutions for both bright and dark nonautonomous solitons governed by the generalized cubic–quintic–septimal nonlinear Schrödinger’s equation with time-dependent coefficients. These soliton solutions exhibit characteristics, including distributed parameters affecting their amplitude, position, and phase, offering effective control over their evolution. Through examination of different material parameters, we observe features in the evolution of these soliton structures, demonstrating the influence of system parameter modulation. Notably, our findings highlight the potential for dynamic control of soliton behavior through adjustments of time-modulated group velocity dispersion and gain or loss parameters.