Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy
solv-int
2009-10-28 v1 Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.solv-int/9407005,
title = {Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy},
author = {Adam Doliwa and Paolo Maria Santini},
journal= {arXiv preprint arXiv:solv-int/9407005},
year = {2009}
}
Comments
LaTeX file, 14 pages + 4 figures