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<p>This article focusses on the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2902_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\((3+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dimensional Yu–Toda–Sassa–Fukuyama (YTSF) model, which is a type of physical model with complex and nonlinear characteristics describing wave propagation in a medium. By using the technique of generalised exponential rational function (GERF), different types of analytical solutions are obtained successfully, including exponential rational solutions, hyperbolic solutions and trigonometric solutions. Subsequently, their dynamic behaviours and temporal-spatial evolutions are investigated through the visualisation of partial solutions. In addition, we discuss the significance of these findings to comprehend nonlinear wave phenomena and outline the future research directions.</p>

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Localised waves and dynamical behaviours of analytical solutions to \((3+1)\)-dimensional YTSF model in mathematical physics

  • 期刊论文

  • 发表日期：

    2025年4月11日

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  • Yajun Du,
  • Jing Pang

摘要

This article focusses on the \((3+1)\) ( 3 + 1 ) -dimensional Yu–Toda–Sassa–Fukuyama (YTSF) model, which is a type of physical model with complex and nonlinear characteristics describing wave propagation in a medium. By using the technique of generalised exponential rational function (GERF), different types of analytical solutions are obtained successfully, including exponential rational solutions, hyperbolic solutions and trigonometric solutions. Subsequently, their dynamic behaviours and temporal-spatial evolutions are investigated through the visualisation of partial solutions. In addition, we discuss the significance of these findings to comprehend nonlinear wave phenomena and outline the future research directions.