<p>Using the zero curvature representation within the framework of Yang-Mills theory, this paper is devoted to exploring geometric properties of the Mikhailov-Lenells system, which was constructed from Lax pairs of two linear <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1075_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">$3\times 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> matrix spectral problems. The Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1075_Article_IEq4.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 initial data being suitably restricted is gauge equivalent to the Mikhailov-Lenells system. This gives a geometric realization of the Mikhailov-Lenells system.</p>

Geometric realization of the Mikhailov-Lenells system on the reductive homogeneous space $GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3$

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2025年5月16日

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Shiping Zhong,
Zehui Zhao,
Jinhuan Wang

摘要

Using the zero curvature representation within the framework of Yang-Mills theory, this paper is devoted to exploring geometric properties of the Mikhailov-Lenells system, which was constructed from Lax pairs of two linear $3\times 3$ $3 \times 3$ matrix spectral problems. The Landau-Lifshitz type model 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 initial data being suitably restricted is gauge equivalent to the Mikhailov-Lenells system. This gives a geometric realization of the Mikhailov-Lenells system.

Geometric realization of the Mikhailov-Lenells system on the reductive homogeneous space \(GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3\)

摘要