Motion of Space Curves in Three-dimensional Minkowski Space R₁³, SO(2,1) Spin Equation and Defocusing Nonlinear Schrödinger Equation

2010/04/22 by Gopal Muniraja, M. Lakshmanan, Muniraja, Gopal +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1004.3856

openalex publication_date 2010/04/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider the dynamics of moving curves in three-dimensional Minkowski space R₁³ and deduce the evolution equations for the curvature and torsion of the curve. Next by mapping a continuous SO(2,1) Heisenberg spin chain on the space curve in R₁³, we show that the defocusing nonlinear Schrödinger equation(NLSE) can be identified with the spin chain, thereby giving a geometrical interpretation of it. The associated linear eigenvalue problem is also obtained in a geometrical way.

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