Dynamical behaviour of solitons and modulation instability analysis of a nonautonomous [formula omitted]-dimensional nonlinear Schrödinger equation

Abstract

This study uses a semi-inverse variational technique to investigate the unknown dynamical behaviour of optical solitons in the solutions of a nonautonomous (1+1)-dimensional nonlinear Schrödinger (NLS) equation. This method produces the bright, anti-bright, and bell-shaped solitons that depend on the delicate balance among the time-dependent spatiotemporal dispersion (STD), group velocity dispersion (GVD), and self-phase modulation (SPM). It is obtained that the soliton solution exists only for non-zero SPM, although the soliton velocity and frequency do not depend on SPM. The soliton amplitude and intensity depends explicitly on time-dependent dispersion and self-phase modulation of the medium. It is found that the focusing medium has a remarkable impact on the intensity of the soliton in comparison to the defocusing, linear, and quadratic nonlinearity. The modulation instability (MI) analysis of the NLS equation has also been investigated using standard linear stability analysis. The explicit dispersion relation has been derived, and MI gain is discussed using different STD, GVD, and SPM coefficients as test functions of time t. The MI gain varies rapidly with the perturbation wave number at a fixed time. The 3D and contour plot of MI gain show that the stability of the NLS equation can be managed significantly by using the time-dependent spatiotemporal, group velocity dispersion, self-phase modulation, wave number, and initial incidence power.