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<p>In this work, we study the high-order true lump solutions of the (2+1)-dimensional three-wave resonant interaction systems using the Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction method. Then we also derive the prediction lump solutions associated with the root structures of the Yablonskii-Vorob’ev polynomial hierarchy and Adler-Moser polynomials under the conditions of large time <i>t</i> and large internal parameters <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11664_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(a_{2m+1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>. We find that the high-order lumps with large internal parameters only generate a displacement without changing their shapes, as time evolves. We further numerically calculate the data-driven lump solutions of the target nonlinear system with the Dirichlet boundary conditions using the slice physics-informed neural network algorithm. Finally, we compare the true lump solutions with analytical prediction solutions as well as data-driven solutions, and show excellent agreement.</p>

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(2+1)-dimensional three-wave resonant interaction systems: Lump pattern and slice physics-informed neural network algorithm

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Xue-Wei Yan,
  • Guang-Yu Gao,
  • Guang-Nan Zhu,
  • Yong Chen

摘要

In this work, we study the high-order true lump solutions of the (2+1)-dimensional three-wave resonant interaction systems using the Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction method. Then we also derive the prediction lump solutions associated with the root structures of the Yablonskii-Vorob’ev polynomial hierarchy and Adler-Moser polynomials under the conditions of large time t and large internal parameters \(a_{2m+1}\) a 2 m + 1 . We find that the high-order lumps with large internal parameters only generate a displacement without changing their shapes, as time evolves. We further numerically calculate the data-driven lump solutions of the target nonlinear system with the Dirichlet boundary conditions using the slice physics-informed neural network algorithm. Finally, we compare the true lump solutions with analytical prediction solutions as well as data-driven solutions, and show excellent agreement.