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 \(N=2\) $N=2$ , 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.