A new two-component nonlinear wave system is studied by the generalized perturbation (\(n,N\hbox {-}n\))-fold Darboux transformation, and various exotic localized vector waves are found. Firstly, the modulational instability is investigated to reveal the mechanism of appearance of rogue waves. Then based on the N-fold Darboux transformation, the generalized perturbation (\(n,N\hbox {-}n\))-fold Darboux transformation is constructed to solve this two-component nonlinear wave system for the first time. Finally, two types of plane-wave seed solutions are selected to explore the localized vector wave solutions such as vector periodic wave solutions, vector breather solutions, vector rogue wave solutions and vector interaction solutions. It is found that there are both localized bright–dark vector waves and bright–bright vector waves in this system, which have not been reported before.

中文翻译：

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两分量非线性波动系统中的局部局部矢量波

通过广义扰动（\（n，N \ hbox {-} n \））的Darboux变换研究了一种新的两分量非线性波系统，发现了各种奇异的局部矢量波。首先，对调制不稳定性进行了研究，以揭示流氓波出现的机理。然后根据N折Darboux变换，得出广义摄动（\（n，N \ hbox {-} n \）构造Darboux变换来首次求解该两分量非线性波动系统。最后，选择两种类型的平面波种子解来探索局部矢量波解，例如矢量周期波解，矢量呼吸解，矢量流浪解和矢量相互作用解。发现该系统中既有局部的明暗矢量波又有明暗矢量波，以前没有报道过。