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<p>The Hirota bilinear equation with variable coefficients (VCs) serves as a fundamental model for capturing nonlinear wave dynamics in fluids and oceans. Utilizing the Hirota bilinear framework alongside advanced symbolic computation techniques, higher-order rational solutions to this equation have been comprehensively investigated. These solutions unveil a wide range of waveforms, including multi-rogue waves (RWs) and multi-parallel solitons. To further expand the solution space, the rational solutions have been generalized by introducing two adjustable parameters, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1292_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1292_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>, referred to as center control parameters. These parameters enable the generation of a versatile class of nonlinear, controllable RWs, enhancing the flexibility and applicability of the model. Soliton solutions have also been constructed using the Wronskian method, with their validity rigorously established through proofs grounded in Plücker relations. By employing various functional forms for the VCs, the dynamic properties of these solutions have been extensively analyzed and visualized through three-dimensional representations, showcasing their rich complexity and diverse behaviors.</p>

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A Study of a (3+1)-Dimensional Hirota Bilinear Model with Variable Coefficients: Generalized Higher-Order Rogue Waves and Wronskian Solutions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月22日

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  • Majid Madadi,
  • Mustafa Inc

摘要

The Hirota bilinear equation with variable coefficients (VCs) serves as a fundamental model for capturing nonlinear wave dynamics in fluids and oceans. Utilizing the Hirota bilinear framework alongside advanced symbolic computation techniques, higher-order rational solutions to this equation have been comprehensively investigated. These solutions unveil a wide range of waveforms, including multi-rogue waves (RWs) and multi-parallel solitons. To further expand the solution space, the rational solutions have been generalized by introducing two adjustable parameters, \(\alpha \) α and \(\beta \) β , referred to as center control parameters. These parameters enable the generation of a versatile class of nonlinear, controllable RWs, enhancing the flexibility and applicability of the model. Soliton solutions have also been constructed using the Wronskian method, with their validity rigorously established through proofs grounded in Plücker relations. By employing various functional forms for the VCs, the dynamic properties of these solutions have been extensively analyzed and visualized through three-dimensional representations, showcasing their rich complexity and diverse behaviors.