On Geometric Realization of the General Manakov System

被引：0
作者：
Qing Ding
Shiping Zhong
机构：
[1] Wenzhou University,Department of Mathematics
[2] Fudan University,School of Mathematical Sciences
[3] Gannan Normal University,School of Mathematics and Computer Sciences
来源：
Chinese Annals of Mathematics, Series B | 2023年 / 44卷
关键词：
Manakov system; Geometric realization; Prescribed curvature representation; 53C30; 53E30; 35Q55; 37K25; 35Q60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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) = kα ⊕ mα (α = 1, 2) and u(3) = k3 ⊕ m3 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.
引用
收藏
页码：753 / 764
页数：11
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