Solitary Wave Solutions for the Nlse with Higher- Order Effects

A higher order nonlinear Schrödinger equation (NLSE) with thirdand fourth-order dispersions, cubic-quintic nonlinearities, self steepening, and self-frequency shift effects is considered. This model describes the propagation of femtosecond light pulses in optical fibers. It is to be noted that soliton pulses are used as the information carriers (elementary "bits") to transmit digital signals over long distances. The complex envelope function ansatz of Li et al. [5] is adopted to investigate general analytic solitary wave solutions and derive explicit bright and dark solitons for the considered model. Importantly, new analytical dark and bright wave solutions expressed in terms of the model coefficients are found. These exact solutions are useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a higher-order nonlinear and dispersive Schrödinger system.