The dynamics, stability and modulation instability of Gaussian beams in nonlocal nonlinear media

We present a rigorous investigation of the dynamics of Gaussian beams in nonlocal nonlinear media with varying degrees of nonlocality. The study includes a stability analysis and modulational instability. The system is represented by the nonlocal nonlinear Schrodinger equation and studied using the Lagrangian variational method and split-step Fourier method. We reveal that as nonlocality increases, the potential well becomes narrower, the soliton oscillation amplitude decreases, and the frequency of soliton oscillation increases. Additionally, we conduct a linear stability analysis and define a stable soliton propagation parametric space. At higher degrees of nonlocality, stable solitons are more resistant to small perturbations, and modulational instability is eliminated. These findings may have practical applications in switching applications and the development of corresponding all-optical devices.