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Breathers and higher order rogue waves on the double-periodic background for the nonlocal Gerdjikov–Ivanov equation

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Abstract

Through Darboux transformation (DT) method, the breathers and the rogue waves on the double-periodic background of the nonlocal Gerdjikov–Ivanov (GI) equation are derived. First, we use the odd-fold DT, the even-fold DT and the plane wave seed solution to obtain some novel solutions for the nonlocal GI equation. These solutions include single- and double-periodic wave, one-breather, and one-breather on the single- or the double-periodic background. Second, we construct the odd-fold semi-degenerate DT and the even-fold semi-degenerate DT to find the higher-order rogue waves on the single-periodic and the double-periodic background, respectively. Finally, the dynamics of above mentioned solutions are analysed graphically by choosing appropriate parametric values.

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Data Availability Statement

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

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11861050 and 11261037), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2020LH01010 and 2022ZD05), the Fundamental Research Funds for the Inner Mongolia Normal University (Grant No. 2022JBTD007, 2022JBXC013), and Graduate Students’ Research and Innovation fund of Inner Mongolia Normal University (Grant Nos. CXJJB22010, CXJJS21119).

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Authors and Affiliations

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

    DongZhu Jiang &  Zhaqilao

  2. Center for Applied Mathematical Science, Inner Mongolia, Hohhot, 010022, People’s Republic of China

    DongZhu Jiang &  Zhaqilao

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  1. DongZhu Jiang
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Jiang, D., Zhaqilao Breathers and higher order rogue waves on the double-periodic background for the nonlocal Gerdjikov–Ivanov equation. Nonlinear Dyn 111, 10459–10472 (2023). https://doi.org/10.1007/s11071-023-08387-w

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