Dynamical behavior and modulation instability of optical solitons with spatio-temporal dispersion

In this paper, we focus on the dynamical behavior and modulation instability of optical solitons with spatiotemporal dispersion for the variable -coefficient nonlinear Schrodinger equation. The expressions of one-soliton solutions are derived, and the dynamical behaviors of one-soliton are studied by selecting the appropriate coefficient functions. Some interesting motion trajectories of solitons under the influence of variable -coefficient functions are revealed. In addition, the distribution of modulation instability (MI) gain versus the power, time and wave number is studied based on the linear stability analysis. The effect of the spatio-temporal dispersion on soliton transmission and gain is characterized. The obtained results are visualized in the 3D space by MATLAB or MAPLE. The results obtained in this paper provide a significant contribution to the formation of optical solitons in nonlinear optical fiber systems or other physical problems.