We present a matrix coupled dispersionless (CD) system. A Lax pair for the matrix CD system is proposed and Darboux transformation is constructed on the solutions of the matrix CD system and the associated Lax pair. We express an N soliton formula for the solutions of the matrix CD system in terms of quasideterminants. By using properties of the quasideterminants, we obtain some exact solutions, including bright and dark-type solitons, rogue wave and breather solutions of the matrix CD system. Furthermore, it has been shown that the solutions of the matrix CD system are expressed in terms of solutions to the usual CD system, sine-Gordon equation and Maxwell–Bloch system.

中文翻译：

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矩阵耦合无色散系统的Darboux变换和精确的多孤子

我们提出了一种矩阵耦合无色散（CD）系统。提出了矩阵CD系统的Lax对，并在矩阵CD系统和相关Lax对的解上构造了Darboux变换。我们用准端基来表示矩阵CD系统的解的N孤子公式。通过使用准端基的性质，我们获得了一些精确的解决方案，包括矩阵CD系统的明暗类型孤子，流氓波和通气解。此外，已经表明，矩阵CD系统的解以普通CD系统，正弦-戈登方程和Maxwell-Bloch系统的解表示。