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<p>Nonlocal integrable nonlinear systems can be used to excite some novel nonlinear phenomena when considering the nonlocal conditions and interactions of fluids. Revealing the dynamic behaviors of shallow-water waves in the ocean, the nonlocal ABKP system in (2+1)-dimensions will be considered in this article. Firstly, the Hirota method is used to establish a standard condition of <i>n</i>-solitons, based on the bilinear equation of Bell’s polynomial theory. Particularly, a series of analyses are conducted on the Hirota condition, resulting in novel wave structures including multi-breather, multi-lump and lump-breather waves. Furthermore, the stability analysis for ABKP system is discussed using the qualitative theory, and a solitary wave solution is presented via Hamilton potential function. Finally, two novel types of exact network model solutions are derived via bilinear neural network approach. All 3-D and 2-D plots effectively illustrate the wave characteristics for the solutions obtained. The methods employed of this study are effective for analyzing the nonlinear dynamics of nonlocal integrable systems. Meanwhile, the results obtained are helpful for further deepening the understanding of nonlinear phenomena in fluid physics or plasma physics.</p>

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The Nonlocal (2+1)-Dimensional ABKP System: Hirota Analysis, Soliton Dynamics and Novel Wave Structures

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Litao Gai,
  • Wenyu Wu,
  • Runfa Zhang

摘要

Nonlocal integrable nonlinear systems can be used to excite some novel nonlinear phenomena when considering the nonlocal conditions and interactions of fluids. Revealing the dynamic behaviors of shallow-water waves in the ocean, the nonlocal ABKP system in (2+1)-dimensions will be considered in this article. Firstly, the Hirota method is used to establish a standard condition of n-solitons, based on the bilinear equation of Bell’s polynomial theory. Particularly, a series of analyses are conducted on the Hirota condition, resulting in novel wave structures including multi-breather, multi-lump and lump-breather waves. Furthermore, the stability analysis for ABKP system is discussed using the qualitative theory, and a solitary wave solution is presented via Hamilton potential function. Finally, two novel types of exact network model solutions are derived via bilinear neural network approach. All 3-D and 2-D plots effectively illustrate the wave characteristics for the solutions obtained. The methods employed of this study are effective for analyzing the nonlinear dynamics of nonlocal integrable systems. Meanwhile, the results obtained are helpful for further deepening the understanding of nonlinear phenomena in fluid physics or plasma physics.