标题： 矢量复数修正Korteweg-de Vries方程的孤子、呼吸子、正则波和 rogue 波 显示英文标题

标题： Soliton,breathers,positons and rogue waves for the vector complex modified Korteweg-de Vries equation

摘要： 本文构建了向量复数修正Korteweg-de Vries（vcmKdV）方程的$N$重Darboux变换（DT），并给出了其行列式表示。 利用DT和多倍特征值退化，我们推导出了vcmKdV方程的全局有界解，包括$N$-亮-亮-亮孤子，$N$-暗-亮-亮孤子， $N$-呼吸子，$N$-正则解，以及$N$阶 rogue wave 解。 所有这些解都是全局有界的。 提供了亮-亮-亮和暗-亮-亮孤子解的图形表示，展示了周期性振荡波与孤子共存或相互作用的现象。 通过渐近分析研究了两亮-亮-亮解的碰撞场景。 图示了有限Akhmediev呼吸子、有限暗-亮孤子呼吸子和呼吸子-呼吸子混合波。 我们给出了正则解、rogue wave 以及与暗-亮孤子和呼吸子混合的rogue wave 的图形。 显示英文摘要

摘要： This paper constructs the $N$-fold Darboux transformation (DT) for the vector complex modified Korteweg-de Vries (vcmKdV) equation and presents its determinant representation. Utilizing the DT and multi-fold eigenvalue degeneracy, we derive globally bounded solutions for the vcmKdV equation, including $N$-bright-bright-bright solitons, $N$-dark-bright-bright solitons, $N$-breathers, $N$-positon solutions, and $N$th-order rogue wave solutions." All these solutions are globally bounded. Graphical representations of bright-bright-bright and dark-bright-bright soliton solutions are provided, illustrating phenomena where periodic oscillatory waves coexist or interact with solitons. The collision scenarios of the two-bright-bright-bright solution have been investigated by using the asymptotic analysis. The bounded Akhmediev breather, the bounded breather with dark-bright soliton and breather-breather mixed waves are graphically shown. We give the graphs of the positon solution, the rogue wave and the rogue wave mixes with dark-bright solitons and breathers.