Central Affine Curve Flow on the Plane
Differential Geometry
2014-05-20 v1 Exactly Solvable and Integrable Systems
Abstract
We give the following results for Pinkall's central affine curve flow on the plane: (i) a systematic and simple way to construct the known higher commuting curve flows, conservation laws, and a bi-Hamiltonian structure, (ii) Baecklund transformations and a permutability formula, (iii) infinitely many families of explicit solutions. We also solve the Cauchy problem for periodic initial data.
Cite
@article{arxiv.1405.4046,
title = {Central Affine Curve Flow on the Plane},
author = {Chuu-Lian Terng and Zhiwei Wu},
journal= {arXiv preprint arXiv:1405.4046},
year = {2014}
}
Comments
to appear in Journal of Fixed Point Theory and Applications (Choquet-Bruhat Festschrift)