Muniraja, Gopal ; Lakshmanan, M. (2010) Motion of space curves in three dimensional Minkowski space R31, SO(2,1) spin equation and defocusing nonlinear Schrödinger equation International Journal of Geometric Methods in Modern Physics, 7 (6). pp. 1043-1049. ISSN 0219-8878
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Official URL: http://www.worldscinet.com/ijgmmp/07/0706/S0219887...
Related URL: http://dx.doi.org/10.1142/S0219887810004701
Abstract
We consider the dynamics of moving curves in three-dimensional Minkowski space R31 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 R31, 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to World Scientific Publishing Company. |
| Keywords: | Minkowski Space; Frenet Equations; So(2; 1) Heisenberg Spin Equation; Defocusing Nonlinear Schrödinger Equation |
| ID Code: | 85037 |
| Deposited On: | 29 Feb 2012 07:05 |
| Last Modified: | 19 May 2016 01:14 |
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