A numerical method for the Hirota equation in a dispersive optical media

In this study, the propagation of ultrashort optical pulses in the context of long-distance optical fiber communications is numerically investigated. The method used is the finite difference scheme in the third order time domain and periodic boundary conditions. As a result, the obtained discrete system of ordinary differential equations is solved numerically by the fourth-order Runge–Kutta algorithm. The proposed algorithm was tested on various input pulses. Precise results of temporal mappings are presented.