Abstract
In this paper, a generalized Darboux transformation for the complex modified Korteweg–de Vries (mKdV) equation is constructed by the Darboux matrix method. As applications, Nth-order wave solutions of the complex mKdV equation have been obtained, part of which exhibit features of rogue waves, such as the first- to third-order rogue waves that are discussed and illustrated through some figures.
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