Dark optical, singular solitons and conservation laws to the nonlinear Schrodinger's equation with spatio-temporal dispersion

This paper studies the dynamics of solitons to the nonlinear Schrodingers equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the RiccatiBernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.