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Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation

Author

Listed:
  • Tianwei Qiu

    (School of Mathematics Sciences, Beihang University, Beijing 100191, China)

  • Zhen Wang

    (School of Mathematics Sciences, Beihang University, Beijing 100191, China
    School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Xiangyu Yang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Guangmei Wei

    (School of Mathematics Sciences, Beihang University, Beijing 100191, China)

  • Fangsen Cui

    (Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore)

Abstract

In this paper, soliton solutions, lump solutions, breather solutions, and lump-solitary wave solutions of a (2+1)-dimensional variable-coefficient extended shallow-water wave (vc-eSWW) equation are obtained based on its bilinear form. By calculating the vector field of the potential function, the interaction between lump waves and solitary waves is studied in detail. Lumps can emerge from the solitary wave and are semi-localized in time. The analytical solutions may enrich our understanding of the nature of shallow-water waves.

Suggested Citation

  • Tianwei Qiu & Zhen Wang & Xiangyu Yang & Guangmei Wei & Fangsen Cui, 2024. "Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation," Mathematics, MDPI, vol. 12(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3054-:d:1488775
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    References listed on IDEAS

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    1. Guang-Mei Wei & Yi-Tian Gao & Wei Hu & Chun-Yi Zhang, 2006. "Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 343-350, October.
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