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<p>Using the Sym-Pohlmeyer reconstruction formula, this paper devotes to exploring geometric properties of two integrable long-wave-short-wave (LWSW) resonance models, including the Yajima–Oikawa system and the Newell system, which appear in fluid mechanics as well as plasma physics. The Landau-Lifshitz-type models of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2436_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="109" /> </InlineMediaObject> <EquationSource Format="TEX">\(GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mi>L</mi> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mo>∗</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mn>3</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> with corresponding initial data being suitably restricted are gauge equivalent to two integrable LWSW resonance models. These results give corresponding geometric realizations of two integrable LWSW resonance models.</p>

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The Long-wave-short-wave Resonance Models and Related Sym-Pohlmeyer Moving Curves

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Shiping Zhong

摘要

Using the Sym-Pohlmeyer reconstruction formula, this paper devotes to exploring geometric properties of two integrable long-wave-short-wave (LWSW) resonance models, including the Yajima–Oikawa system and the Newell system, which appear in fluid mechanics as well as plasma physics. The Landau-Lifshitz-type models of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space \(GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3\) G L ( 3 , C ) / ( C ∗ ) 3 with corresponding initial data being suitably restricted are gauge equivalent to two integrable LWSW resonance models. These results give corresponding geometric realizations of two integrable LWSW resonance models.