The Integrable Dynamics of Discrete and Continuous Curves

Details The Integrable Dynamics of Discrete and Continuous Curves The Integrable Dynamics of Discrete and Continuous Curves

1994-12-30

arxiv.org/abs/solv-int/9501001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, LaTeX file, 4 ps figures

Scientific paper

We show that the following geometric properties of the motion of discrete and continuous curves select integrable dynamics: i) the motion of the curve takes place in the N dimensional sphere of radius R, ii) the curve does not stretch during the motion, iii) the equations of the dynamics do not depend explicitly on the radius of the sphere. Well known examples of integrable evolution equations, like the nonlinear Schroedinger and the sine-Gordon equations, as well as their discrete analogues, are derived in this general framework.

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