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

Adam Doliwa; Paolo Maria Santini

doi:10.1063/1.531119

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

Adam Doliwa·Paolo Maria Santini

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Abstract

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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Adam Doliwa, Paolo Maria Santini. 1994-07-27. Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy. https://doi.org/10.1063/1.531119

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