Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-04-22
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Accepted in International Journal of Geometric Methods in Modern Physics
Scientific paper
We consider the dynamics of moving curves in three-dimensional Minkowski space $R_1^{3}$ 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 $R_1^{3}$, we show that the defocusing nonlinear Schr\"odinger 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.
Lakshmanan Meenakshi
Muniraja Gopal
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