Abstract
We construct new exact solutions of the extended mKdV (emKdV) equation. The exact solutions are obtained by nonlinearization of spectral problem associated with the travelling periodic waves and using the one-fold, two-fold Darboux transformations. We consider the dnoidal and cnoidal travelling periodic waves of the emKdV equation. Since the dnoidal travelling periodic wave is modulationally stable, the algebraic solitons propagating on dnoidal wave background. However, since the cnoidal travelling periodic wave is modulationally unstable, the rogue waves generated on the cnoidal wave background.
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