Optical solitons to the nonlinear Shrödinger’s equation with spatio-temporal dispersion using complex amplitude ansatz

In this work, we investigate the optical solitons to the non-linear Shrödinger’s equation with spatio-temporal dispersion. There are two types of non-linear media studied in this paper. They are Kerr law and parabolic law. By adopting a complex amplitude ansatz method composed of the addition of bright and dark optical solitons, we present the exact dark, bright and dark-bright or combined optical solitons to the model. Numerical results and discussions are also presented.