Abstract
We construct rogue wave solutions of the complex modified Korteweg–de Vries (cmKdV) equation with higher-order effects on the periodic background. The rogue waves are obtained by nonlinearization of spectral problem associated with the travelling periodic waves and using the one-fold Darboux transformation. We consider the dnoidal and cnoidal travelling periodic waves as the seed solutions. Since the dnoidal and cnoidal travelling periodic waves are modulationally unstable as regards long wave perturbations, the rogue waves generated on the periodic background.
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