On Geometric Realization of the Discrete Manakov Equation of Mixed Type

Abstract

The authors introduce the coupled discrete 2-component nonlinear Schrödinger equation with M-solutions and prove that this type of discrete equation is an integrable discretization of the integrable Manakov equation of mixed type. Moreover, the integrable discrete equation of 1-d Schrödinger flow to the pseudo-projective 2-space U(2, 1)/U(1, 1) × U(1) is shown to be a geometric realization of the integrable discrete Manakov equation of mixed type.

Keywords

Manakov equation / Geometric realization / Integrable discretization / 53C30 / 53E30 / 35Q55 / 37K25 / 35Q60

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