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Rogue periodic waves and hybrid nonlinear waves in the \((2+1)\)-dimensional CDGKS equation

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Abstract

The \((2+1)\)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation is decomposed into two \((1+1)\)-dimensional soliton equations in the modified Korteweg–de Vries (mKdV) hierarchy. With the aid of the decomposition, two rogue wave solutions to the CDGKS equation on the background of Jacobian elliptic functions dn and cn are derived by combining nonlinearization of the mKdV spectral problem and an N-fold Darboux transformation. Besides, the hybrid solutions of soliton and breather in the CDGKS equation is also presented by the N-fold Darboux transformation. In particular, the dynamical behavior of the CDGKS equation are illustrated through some figures. The  paper   enriches   the rogue wave solution structure of the higher dimensional nonlinear evolution equation on the periodic wave background.

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The authors declare that all data supporting the findings of this study are available within the article.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11971322, 11861050), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2020LH01010, 2020LH01008 and 2022ZD05) and the Fundamental Research Funds for the Inner Mongolia Normal university (Grant No. 2022JBTD007, 2022JBZD011).

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Authors and Affiliations

  1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Wurile,  Taogetusang &  Zhaqilao

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People’s Republic of China

    Chun-Xia Li

  3. Applied Mathematics Center of Inner Mongolia, Hohhot, 010022, People’s Republic of China

    Wurile,  Taogetusang &  Zhaqilao

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  1. Wurile
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Correspondence to Zhaqilao.

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Wurile, Taogetusang, Li, CX. et al. Rogue periodic waves and hybrid nonlinear waves in the \((2+1)\)-dimensional CDGKS equation. Nonlinear Dyn 111, 13425–13438 (2023). https://doi.org/10.1007/s11071-023-08539-y

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