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<p>This article presents the unique analysis of an integrable (3+1)-dimensional shallow water wave equation with potential implications in ocean engineering, marine environments, atmospheric research, and other fields. The paper explored the derivation of lump, multi-peakons, and soliton solutions using a recently developed technique: the generalized exponential differential rational function method that relies on a trial solution of an ordinary differential equation, involving the exponential rational function’s ith derivative. To examine the physical characteristics of the obtained solutions, the results are presented visually through 3D surface plots and density plots, offering a clear understanding of the wave dynamics. The findings provide crucial insights into complex wave behavior, particularly in the context of shallow water and nonlinear wave interactions.</p>

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Extraction of Lumps, Solitons, and Multi-Peakons for an Integrable Shallow Water Wave Equation

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Nauman Raza,
  • Asifa Zahid,
  • M. Higazy,
  • Ahmet Bekir,
  • Y. S. Hamed

摘要

This article presents the unique analysis of an integrable (3+1)-dimensional shallow water wave equation with potential implications in ocean engineering, marine environments, atmospheric research, and other fields. The paper explored the derivation of lump, multi-peakons, and soliton solutions using a recently developed technique: the generalized exponential differential rational function method that relies on a trial solution of an ordinary differential equation, involving the exponential rational function’s ith derivative. To examine the physical characteristics of the obtained solutions, the results are presented visually through 3D surface plots and density plots, offering a clear understanding of the wave dynamics. The findings provide crucial insights into complex wave behavior, particularly in the context of shallow water and nonlinear wave interactions.