On Geometric Realization of the General Manakov System

Abstract

It is well-known that the general Manakov system is a 2-components nonlinear Schrödinger equation with 4 nonzero real parameters. The analytic property of the general Manakov system has been well-understood though it looks complicated. This paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills’ theory. Three models of moving curves evolving in the symmetric Lie algebras u(2,1) = k _α ⊕ m _α (α = 1, 2) and u(3) = k ₃ ⊕ m ₃ are shown to be simultaneously the geometric realization of the general Manakov system. This reflects a new phenomenon in geometric realization of a partial differential equation/system.

Keywords

Manakov system / Geometric realization / Prescribed curvature representation

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