Central Affine Curve Flow on the Plane
arXiv:1405.4046
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.
to appear in Journal of Fixed Point Theory and Applications (Choquet-Bruhat Festschrift)