Hasimoto variables, generalized vortex filament equations, Heisenberg models and Schrodinger maps arising from group-invariant NLS systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:144

Article

Anco, Stephen C.¹  Asadi, Esmaeel² 

[1] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada

[2] IASBS, Dept Math, Zanjan 4513766731, Iran

关键词: Geometric curve flow;    Integrable systems;    lsospectral flow;    Vortex filament equation;    Heisenberg spin model;    Schrodinger map;   

DOI  :  10.1016/j.geomphys.2019.06.010

来源: Elsevier

【 摘 要 】

The deep geometrical relationships holding among the NLS equation, the vortex filament equation, the Heisenberg spin model, and the Schrodinger map equation are extended to the general setting of Hermitian symmetric spaces. New results are obtained by utilizing a generalized Hasimoto variable which arises from applying the general theory of parallel moving frames. The example of complex projective space CPN = SU(N +1)/U(N) is used to illustrate the method and results. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free