Dark soliton solutions of the defocusing Hirota equation by the binary Darboux transformation

Abstract

In this paper, we study the defocusing Hirota equation that describes the propagation of ultrashort pulses in optical fibers with third-order dispersion and self-steepening higher-order effects. By the limit technique, we construct the Nth-iterated binary Darboux transformation in the determinant form and present a complete proof. We derive the multi-dark soliton solutions from the nonzero background and discuss the properties of dark solitons through the figures for several sample solutions. Our results will be valuable to the study of the future development of dark solitons in long-distance optical communication system.