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On Geometric Realization of the General Manakov System

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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) = 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.

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Authors and Affiliations

  1. Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang, 325035, China

    Qing Ding

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Qing Ding

  3. School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000, Jiangxi, China

    Shiping Zhong

Authors
  1. Qing Ding
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  2. Shiping Zhong
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Corresponding authors

Correspondence to Qing Ding or Shiping Zhong.

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Conflicsts of interest The authors declare no conflicts of interest.

Additional information

This work was supported by the 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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Ding, Q., Zhong, S. On Geometric Realization of the General Manakov System. Chin. Ann. Math. Ser. B 44, 753–764 (2023). https://doi.org/10.1007/s11401-023-0042-9

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  • DOI: https://doi.org/10.1007/s11401-023-0042-9

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