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<p>Under investigation in this paper is a (2+1)-dimensional variable-coefficient breaking soliton equation in fluids and plasmas. Bilinear forms, one-, two- and three-soliton solutions are derived via Hirota method. Velocity and shape of the soliton can be influenced by the dispersion coefficients <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2024_10810_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha (t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2024_10810_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta (t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, while the amplitude of the soliton can not be affected. Interactions between the two and among the three solitons are graphically discussed: the soliton has the phase shift without any influence on its shape and amplitude after the interaction, indicating that the interaction between the solitons is elastic. The stability of the soliton is studied numerically by considering truncation errors as small perturbations, which shows the soliton propagates steadily under the small perturbations.</p>

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Soliton stability and numerical simulation for the (2+1)-dimensional variable-coefficient breaking soliton equation in fluids and plasmas

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Cong-Cong Hu

摘要

Under investigation in this paper is a (2+1)-dimensional variable-coefficient breaking soliton equation in fluids and plasmas. Bilinear forms, one-, two- and three-soliton solutions are derived via Hirota method. Velocity and shape of the soliton can be influenced by the dispersion coefficients \(\alpha (t)\) α ( t ) and \(\beta (t)\) β ( t ) , while the amplitude of the soliton can not be affected. Interactions between the two and among the three solitons are graphically discussed: the soliton has the phase shift without any influence on its shape and amplitude after the interaction, indicating that the interaction between the solitons is elastic. The stability of the soliton is studied numerically by considering truncation errors as small perturbations, which shows the soliton propagates steadily under the small perturbations.