Dispersive optical solitons with Schrödinger-Hirota equation by a couple of integration schemes

The perturbed nonlinear Schrödinger-Hirota equation with spatio-temporal dispersion that governs the propagation of dispersive pulses in optical fibers is investigated in this study using three methods that are the Csch method, Tanh-Coth method and modified simple equation method. The Kerr and power laws of nonlinearity are taken into account. Bright soliton, dark soliton, singular soliton, mixed bright-dark soliton and periodic solutions are retrieved. Many constraint conditions required for the existence of solutions emerge from the integration methods. Furthermore, we demonstrate the dynamical behaviors and physical significance of these solutions by using different parameter values.