Abstract
This paper considers the coupled complex modified Korteweg‐de Vries (mKdV) equations and presents a binary Darboux transformation for the equations. As a direct application, we give a classification of general soliton solutions derived from vanishing and non‐vanishing backgrounds, on the basis of the dynamical behavior of the solutions. Special types of solutions in the presented solutions include breathers, bright‐bright solitons, bright‐dark solitons, bright‐W‐shaped solitons, and rogue wave solutions. Furthermore, dynamics and interactions of vector bright solitons are exhibited.
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