Geometric realization of the Mikhailov-Lenells system on the reductive homogeneous space GL(3,C)/(C∗)3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GL(3,{\mathbb {C}})/({\mathbb {C}}^*)^3$$\end{document}Geometric realization of the Mikhailov-Lenells system on the...S. Zhong et al.

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 3×3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 3$$\end{document} matrix spectral problems. The Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space GL(3,C)/(C∗)3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GL(3,\mathbb C)/({\mathbb {C}}^*)^3$$\end{document} with initial data being suitably restricted is gauge equivalent to the Mikhailov-Lenells system. This gives a geometric realization of the Mikhailov-Lenells system.