In this article, we formulate a determinant representation of the Darboux transformation for the Kulish–Sklyanin (KS) model, which can be viewed as a generalization of the nonlinear Schrödinger equation, and obtain a new compact formula of $n$-soliton solution for the KS system. As applications of the formula, the abundant dynamics of one-, two- and three-soliton solutions for the case $m=2$ are discussed. The different structures of soliton solitons are obtained by setting different parameters.

中文翻译：

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Kulish-Sklyanin 模型的 Darboux 变换的行列式表示和 m=2 的新孤子解

在本文中，我们为 Kulish-Sklyanin (KS) 模型制定了 Darboux 变换的行列式表示，可以将其视为非线性薛定谔方程的推广，并获得了一个新的紧凑公式 $n$-KS系统的孤子解决方案。作为公式的应用，案例的一、二和三孤子解的丰富动力学$米=2$进行了讨论。通过设置不同的参数，可以得到不同结构的孤子孤子。