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General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation

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Abstract

In this work, the (2+1)-dimensional Korteweg-de Vries equation is investigated, which can be used to represent the amplitude of the shallow–water waves in fluids or electrostatic wave potential in plasmas. By employing the properties of Bell’s polynomial, we obtain bilinear representation of the equation with the aid of an appropriate transformation. Based on the obtained Hirota bilinear form, its lump solutions with localized characteristics are constructed in detail. We then derive the lumpoff solutions of the equation by studying a soliton solution generated by lump solutions. Furthermore, special rogue wave solutions with predictability are well presented, and the time and place of appearance are also derived. Finally, some graphic analysis is represented to better understand the propagation characteristics of the obtained solutions. It is hoped that our results provided in this work can be used to enrich the dynamic behaviors of the equation.

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Acknowledgements

We express our sincere thanks to the Editor and Reviewers for their valuable comments. This work was supported by the Postgraduate Research and Practice of Educational Reform for Graduate students in CUMT under Grant No. 2019YJSJG046, the Natural Science Foundation of Jiangsu Province under Grant No. BK20181351, the Six Talent Peaks Project in Jiangsu Province under Grant No. JY-059, the Qinglan Project of Jiangsu Province of China, the National Natural Science Foundation of China under Grant Nos. 11975306 and 61877053, the Fundamental Research Fund for the Central Universities under the Grant Nos. 2019ZDPY07 and 2019QNA35, and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.

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Authors and Affiliations

  1. School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Hui Wang, Shou-Fu Tian, Tian-Tian Zhang & Yi Chen

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yong Fang

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  1. Hui Wang
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  2. Shou-Fu Tian
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  3. Tian-Tian Zhang
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  4. Yi Chen
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Correspondence to Shou-Fu Tian, Tian-Tian Zhang or Yong Fang.

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Wang, H., Tian, SF., Zhang, TT. et al. General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation. Comp. Appl. Math. 38, 164 (2019). https://doi.org/10.1007/s40314-019-0938-x

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