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

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Preprint

27 July 1994

preprint
Published by arXiv in arXiv

DOI:10.48550/arXiv.solv-int/9407005

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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Version 1, 1994-07-27, ArXiv
Published version: Journal of Mathematical Physics, 36 (3), 1259.

This publication has 2 references indexed in Scilit:

Integrable functional equations and algebraic geometry
Duke Mathematical Journal, 1994
Solitons and the Inverse Scattering Transform
1981