Propagation of chirped gray solitons in weakly nonlocal media with parabolic law nonlinearity and spatio-temporal dispersion

In our research, we have examined the existence and stability of chirped periodic and solitary waves in a weakly nonlocal nonlinear medium, which exhibits various types of effects, including inter-modal dispersion, nonlinear dispersion, detuning, spatio-temporal, and parabolic law nonlinearity. By studying the nonlinear Schrödinger equation that describes the field dynamics in this system, a class of nonlinearly chirped periodic waves is derived in the presence of all physical processes. In addition, we have obtained solitary waves of the gray type in the long-wave limit of these nonlinear waveforms. We have found that the frequency chirp associated with these optical waves depends on their intensity and its magnitude can be controlled by manipulating the nonlinear dispersion parameter. Furthermore, we have numerically studied the stability of the gray soliton solution under finite initial perturbations. Our results indicate that the nonlinear waves we have identified represent new types of extremely robust chirped localized structures in weakly nonlocal nonlinear parabolic law media.