Scholarlink

<p>A system coupling the cubic, nonlinear Schrodinger equation (NLS) and the Korteweg–de Vries equation (KdV) commonly known as the NLS–KdV system was previously analysed to be inconsistently derived and a few alternative systems were proposed as more suitable models for describing the interaction of long and short waves in dispersive media (Deconinck et al. in J Phys A: Math Theor 49:415501, 2016. <a href="https://doi.org/10.1088/1751-8113/49/41/415501">https://doi.org/10.1088/1751-8113/49/41/415501</a>; Nguyen and Liu in Water Waves 2:327–359, 2020. <a href="https://doi.org/10.1007/s42286-020-00038-6">https://doi.org/10.1007/s42286-020-00038-6</a>; Commun Math Sci 21(3):641–669, 2023. <a href="https://doi.org/10.4310/CMS.2023.v21.n3.a3">https://doi.org/10.4310/CMS.2023.v21.n3.a3</a>). In this manuscript, these alternative systems are shown to possess synchronized solitary waves via the method of constrained minimization, as well as by direct computation of the associated systems of ODEs. These synchronized solitary waves have the hyperbolic <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42286_2025_110_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{sech}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>sech</mtext> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-profile typical of dispersive equations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Explicit Synchronized Solitary Waves for Some Models for the Interaction of Long and Short Waves in Dispersive Media

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年1月27日

查看全文
  • Bruce Brewer,
  • Chuangye Liu,
  • Nghiem V. Nguyen

摘要

A system coupling the cubic, nonlinear Schrodinger equation (NLS) and the Korteweg–de Vries equation (KdV) commonly known as the NLS–KdV system was previously analysed to be inconsistently derived and a few alternative systems were proposed as more suitable models for describing the interaction of long and short waves in dispersive media (Deconinck et al. in J Phys A: Math Theor 49:415501, 2016. https://doi.org/10.1088/1751-8113/49/41/415501; Nguyen and Liu in Water Waves 2:327–359, 2020. https://doi.org/10.1007/s42286-020-00038-6; Commun Math Sci 21(3):641–669, 2023. https://doi.org/10.4310/CMS.2023.v21.n3.a3). In this manuscript, these alternative systems are shown to possess synchronized solitary waves via the method of constrained minimization, as well as by direct computation of the associated systems of ODEs. These synchronized solitary waves have the hyperbolic \(\textrm{sech}^2\) sech 2 -profile typical of dispersive equations.