Integrable surfaces induced by generalized Landau-Lifshitz equation with self-consistent potential

Abstract

In this paper, we present integrable surfaces associated with generalized LandauLifshitz equation with self-consistent potential. We obtained the first and second fundamental forms. The first fundamental form allow us to calculate the curvature and metric properties of a surface, particularly, length and area of related space. The second fundamental form determines the external geometry of the surface in the vicinity of this point. Together they permit to define extrinsic invariants of the surface and its principal curvatures. The results can be used to describe spin waves in magnets and ferromagnets.