Binary Darboux transformation and N-dark solitons for the defocusing Kundu-Eckhaus equation in an optical fiber

In this paper, we focus our attention on the defocusing Kundu-Eckhaus equation, which depicts the propagation of the ultra-short optical pulses in an optical fiber. With respect to the complex envelope of an electromagnetic wave, an N-fold binary Darboux transformation (DT) in the determinant form is constructed, where N is a positive integer. Via the limit technique, determinant operations and obtained N-fold binary DT, we derive the single dark soliton and then perform the N-dark solitons asymptotic analysis. Asymptotic expressions of the dark soliton components at the neighbouring areas along the characteristic lines are obtained, from which we can learn their dynamic properties. When N=2 , we take the 2-dark solitons as the example and graphically illustrate them, which are consistent with the above analytical results. This work may provide a physical mechanism for the generations and interactions of the optical dark solitons in the optical fibers.