In this paper, we obtain two types of semi-rational solutions for a coupled nonlinear Schrödinger equation by applying generalized Darboux transformation (DT). Firstly, we obtain a new DT through a special limit process based on the traditional DT for the equation; then, some nonlinear wave interactions on the zero-intensity background are analyzed under the research of those semi-rational solutions. Based on the above discussion, the dynamics of the interactions between one regular soliton and the type-I degenerate solitons on the zero-intensity background are systematically analyzed by drawing the 3D- and 2D-dimensional plots.

中文翻译：

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耦合非线性Schrödinger方程的广义Darboux变换，半理性解和新颖的简并孤子解

在本文中，我们通过应用广义Darboux变换（DT）获得了耦合非线性Schrödinger方程的两种半有理解。首先，我们根据传统的DT方程，通过特殊的极限过程获得了新的DT；然后，在这些半理性解的研究下，分析了零强度背景下的一些非线性波相互作用。基于以上讨论，通过绘制3D和2D三维图，系统地分析了一个常规孤子与I型简并孤子在零强度背景下相互作用的动力学。