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<p>Yu-Toda-Sasa-Fukuyama (YTSF) equation belongs to the class of Kadomtsev-Petviashvili type integrable systems, which can be applied to describe the nonlinear waves in the fluids, plasmas and other fields. In this paper, we study the <i>M</i>-lump solutions and hybrid solutions with soliton and breather of a generalized YTSF equation. Based on the Hirota bilinear method and long wave limit method, the propagation and interaction of local waves are analyzed graphically. Furthermore, we demonstrate the influence of the parameters on the dynamical properties of these nonlinear waves. The value of wave number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11223_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(k_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> determines the waveform and amplitude of local waves, and the value of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11223_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(w_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>w</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> affects the shape and rotation direction of the lump waves. In addition, the velocity components in the <i>x</i>, <i>y</i> and <i>z</i> directions and wave height of the lump solutions are calculated. The collision properties of the waves are explored, and it is found that a single wave can split into multiple waves, and similarly multiple waves can fuse into a single wave.</p>

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Propagation and interaction of local waves for a generalized Yu-Toda-Sasa-Fukuyama equation in fluids

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Xiao-Hong Yu,
  • Da-Wei Zuo

摘要

Yu-Toda-Sasa-Fukuyama (YTSF) equation belongs to the class of Kadomtsev-Petviashvili type integrable systems, which can be applied to describe the nonlinear waves in the fluids, plasmas and other fields. In this paper, we study the M-lump solutions and hybrid solutions with soliton and breather of a generalized YTSF equation. Based on the Hirota bilinear method and long wave limit method, the propagation and interaction of local waves are analyzed graphically. Furthermore, we demonstrate the influence of the parameters on the dynamical properties of these nonlinear waves. The value of wave number \(k_{i}\) k i determines the waveform and amplitude of local waves, and the value of \(w_{i}\) w i affects the shape and rotation direction of the lump waves. In addition, the velocity components in the x, y and z directions and wave height of the lump solutions are calculated. The collision properties of the waves are explored, and it is found that a single wave can split into multiple waves, and similarly multiple waves can fuse into a single wave.