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<p>In this paper, we investigate dynamics and exact solutions of the traveling wave system of Rosenau-Hyman’s <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1376_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="80" /> </InlineMediaObject> <EquationSource Format="TEX">\(K(-2, -2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo stretchy="false">(</mo> <mo>-</mo> <mn>2</mn> <mo>,</mo> <mo>-</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> equation. Under given parameter conditions, bifurcations of phase portraits in the trvaling wave system are revealed. Corresponding to all bounded solutions of the traveling wave system, 16 explicit exact parametric representations are derived.</p>

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Dynamics and Exact Traveling Wave Solutions of Rosenau-Hyman’s \(K(-2, -2)\) Equation

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Yanfei Dai,
  • Jibin Li

摘要

In this paper, we investigate dynamics and exact solutions of the traveling wave system of Rosenau-Hyman’s \(K(-2, -2)\) K ( - 2 , - 2 ) equation. Under given parameter conditions, bifurcations of phase portraits in the trvaling wave system are revealed. Corresponding to all bounded solutions of the traveling wave system, 16 explicit exact parametric representations are derived.