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Diversity of Interaction Solutions of a Shallow Water Wave Equation

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  • Jian-Ping Yu
  • Wen-Xiu Ma
  • Bo Ren
  • Yong-Li Sun
  • Chaudry Masood Khalique

Abstract

In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions, which can be applied to generate many important solutions, such as lumps and lump-soliton solutions. This is an interesting feature of this research. In addition, we prove this new model is integrable in Painlevé sense. Finally, the diversity of interactive wave solutions of the gHSI is graphically displayed by selecting specific parameters. All the obtained results can be applied to the research of fluid dynamics.

Suggested Citation

  • Jian-Ping Yu & Wen-Xiu Ma & Bo Ren & Yong-Li Sun & Chaudry Masood Khalique, 2019. "Diversity of Interaction Solutions of a Shallow Water Wave Equation," Complexity, Hindawi, vol. 2019, pages 1-6, November.
    • Handle: RePEc:hin:complx:5874904
    DOI: 10.1155/2019/5874904
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