In this paper, we introduce a pseudo-symmetry hypothesis, under which the $N$-fold binary Darboux transformation for the $n$th-order ($n=-1,0,1,\dots$) Ablowitz–Kaup–Newell–Segur (AKNS) system is presented in a unified form. Through the $N$-fold ($N=1,2,3,\dots$) binary Darboux transformation, several high-order analytical solutions of certain nonlinear evolution equations can be obtained based on simple seed solutions. Especially, we take the well-known AB system as an example to present the $N$th-order solitons. Moreover, the obtained results would be helpful to the developments of some computation algorithms on solving the nonlinear evolution equations.

在本文中，我们引入了一个伪对称假设，在该假设下， $N$-fold 二元 Darboux 变换 $n$三阶（$n=-1,0,1,\dots$) Ablowitz-Kaup-Newell-Segur (AKNS) 系统以统一的形式呈现。通过$N$-折叠 （$N=1,2,3,\dots$) 二元达布变换，基于简单的种子解可以得到某些非线性演化方程的几个高阶解析解。特别是，我们以著名的AB系统为例来介绍$N$三阶孤子。此外，所获得的结果将有助于一些求解非线性演化方程的计算算法的发展。