Determinant representation of N-times Darboux transformation for the defocusing nonlinear Schr?dinger equation

摘要

The determinant expression T[N] of a new Darboux transformation (DT) for the Ablowitz-Kaup-Newell-Segur equation are given in this paper. By making use of this DT under the reduction r = q*, we construct determinant expressions of dark N-soliton solution for the defocusing NLS equation. Except known one-soliton, we provide smooth two-soliton and smooth N-soliton on a certain domain of parameter for the defocusing NLS equation.