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

Abstract

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 \(3\times 3\) matrix spectral problems. The Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the reductive homogeneous space \(GL(3,\mathbb C)/({\mathbb {C}}^*)^3\) with initial data being suitably restricted is gauge equivalent to the Mikhailov-Lenells system. This gives a geometric realization of the Mikhailov-Lenells system.