Abstract
Under consideration in this paper is rogue waves on the general periodic traveling wave background of an integrable extended modified Korteweg–de Vries equation. The general periodic traveling wave solutions are presented. By means of the Darboux transformation and the nonlinearization of the Lax pair, we present the first‐, second‐ and third‐order rogue waves on the general periodic traveling wave background. Furthermore, the dynamic behaviors of rogue periodic waves are elucidated from the viewpoint of three‐dimensional structures.
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