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Multi-lump or lump-type solutions to the generalized KP equations in \((N+1)\)-dimensions

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Abstract

We aim to explore lump or lump-type solutions to the generalized Kadomtsev–Petviashvili (gKP) equations in \((N+1)\)-dimensions via the long wave limit technique. The construction procedure for presenting lump or lump-type solutions is improved. The key step is that all the involved parameters are extended to the complex field. We first furnish lump solutions from the corresponding soliton solutions to the \((2+1)\)-dimensional gKP equation. In particular, a general class of multi-lump solutions of the \((2+1)\)-dimensional gKP equation can be obtained. It is then shown that there exist lump-type solutions to the \((N+1)\)-dimensional gKPI equations with \(N \ge 3\) by means of the improved long wave limit technique.

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Acknowledgements

The authors express their sincere thanks to the Referees and Editors for their valuable comments. This work is supported by the National Natural Science Foundation of China (No. 51771083).

Author information

Authors and Affiliations

  1. Normal School, Jinhua Polytechnic, Jinhua, 321007, Zhejiang, China

    Li Cheng & Jian-Ya Ge

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Yi Zhang & Wen-Xiu Ma

  3. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Wen-Xiu Ma

  4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Wen-Xiu Ma

  5. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Wen-Xiu Ma

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

    Wen-Xiu Ma

  7. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

Authors
  1. Li Cheng
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  2. Yi Zhang
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  3. Wen-Xiu Ma
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  4. Jian-Ya Ge
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Correspondence to Li Cheng.

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Cheng, L., Zhang, Y., Ma, WX. et al. Multi-lump or lump-type solutions to the generalized KP equations in \((N+1)\)-dimensions. Eur. Phys. J. Plus 135, 379 (2020). https://doi.org/10.1140/epjp/s13360-020-00366-z

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00366-z

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