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.
arXiv commentto appear in Journal of Fixed Point Theory and Applications (Choquet-Bruhat Festschrift)