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Rogue waves on the periodic background in the extended mKdV equation

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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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This manuscript has no associated data or the data will not be deposited. [Authors’ comment:The data generated during the current study will be made available at reasonable request.]

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  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Yanpei Zhen

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  1. Yanpei Zhen
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Zhen, Y. Rogue waves on the periodic background in the extended mKdV equation. Eur. Phys. J. B 96, 20 (2023). https://doi.org/10.1140/epjb/s10051-023-00489-z

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