Integrable Flows for Starlike Curves in Centroaffine Space
Exactly Solvable and Integrable Systems
2013-03-07 v1 Analysis of PDEs
Differential Geometry
Abstract
We construct integrable hierarchies of flows for curves in centroaffine through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in induces the Kaup-Kuperschmidt hierarchy at the curvature level.
Cite
@article{arxiv.1303.1259,
title = {Integrable Flows for Starlike Curves in Centroaffine Space},
author = {Annalisa Calini and Thomas Ivey and Gloria Mari Beffa},
journal= {arXiv preprint arXiv:1303.1259},
year = {2013}
}