Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion

By using the sub-equation method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving the beta-derivative. This equation describing the propagation of ultra-short optical solitons through parabolic law medium. Nonlinear perturbations of higher-order and self-steepening terms are taken into account. As a result, some new exact solutions are constructed under constraint conditions.