From Euler's elastica to the mKdV hierarchy, through the Faber polynomials
Mathematical Physics
2016-09-21 v1 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
The modified Korteweg-de Vries hierarchy (mKdV) is derived by imposing isometry and isoenergy conditions on a moduli space of plane loops. The conditions are compared to the constraints that define Euler's elastica. Moreover, the conditions are shown to be constraints on the curvature and other invariants of the loops which appear as coefficients of the generating function for the Faber polynomials.
Keywords
Cite
@article{arxiv.1511.08658,
title = {From Euler's elastica to the mKdV hierarchy, through the Faber polynomials},
author = {Shigeki Matsutani and Emma Previato},
journal= {arXiv preprint arXiv:1511.08658},
year = {2016}
}
Comments
14 pages