On Geometric Realization of the General Manakov System

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 sys...

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Bibliographic Details
Published in:Chinese annals of mathematics. Serie B 2023-09, Vol.44 (5), p.753-764
Main Authors: Ding, Qing, Zhong, Shiping
Format: Article
Language:English
Subjects:
Applications of Mathematics
Differential geometry
Lie groups
Mathematics
Mathematics and Statistics
Partial differential equations
Schrodinger equation
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Summary: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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-023-0042-9