Optical soliton solutions of nonlinear Schrödinger equation with second order spatiotemporal dispersion and its modulation instability

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with the coefficients of group velocity dispersion, second-order spatiotemporal dispersion and cubic nonlinearity for illustrating pulse phenomena ahead of the conventional gradually varying envelope approximation. In this paper, we constructed solitary wave and solitons solutions of higher order NLSE by applying proposed F-expansion method. The achieved solitons solutions have vital applications in applied physics. The control technology of optical solitons have been the applications of signal routing, all-optical switching and all-optical shaping. The modulation instability analysis is utilized to investigate the model stability, which verifies that all achieved solutions are exact and stable. We also presented graphically the movement of achieved exact solitons and solitary wave solutions, which helps to know the physical phenomena's of this model. In applied sciences, numerous others such type of arising models can be solved by employing this effective, reliable and powerful technique.