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| On Geometric Realization of the General Manakov System* |
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Citation： |
Qing DING,Shiping ZHONG.On Geometric Realization of the General Manakov System*[J].Chinese Annals of Mathematics B,2023,44(5):753~764 |
| Page view： 930
Net amount： 707 |
Authors： |
Qing DING; Shiping ZHONG |
Foundation： |
National Natural Science Foundation of China (Nos. 12071080,12141104), the Science Technology Project of Jiangxi Educational Committee (No. GJJ2201202) and the Natural Science Foundation of Jiangxi Province (Nos. 20212BAB211005, 20232BAB201006). |
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| Abstract： |
It is well-known that the general Manakov system is a 2-components nonlinear Schr¨odinger 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. |
Keywords： |
Manakov system, Geometric realization, Prescribed curvature representation |
Classification： |
53C30, 53E30, 35Q55, 37K25, 35Q60 |
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