Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy

Details Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy

1994-07-27

arxiv.org/abs/solv-int/9407005v1

J. Math. Phys. 36 (1995) 1259

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX file, 14 pages + 4 figures

Scientific paper

10.1063/1.531119

We show that the following elementary geometric properties of the motion of a discrete (i.e. piecewise linear) curve select the integrable dynamics of the Ablowitz-Ladik hierarchy of evolution equations: i) the set of points describing the discrete curve lie on the sphere S^3, ii) the distance between any two subsequant points does not vary in time, iii) the dynamics does not depend explicitly on the radius of the sphere. These results generalize to a discrete context our previous work on continuous curves.

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