From Euler's elastica to the mKdV hierarchy, through the Faber polynomials

2015/11/27 by Shigeki Matsutani, Emma Previato · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.DG #math.MP #nlin.SI

paper · pdf · doi:10.1063/1.4961690

14 pages

arxiv created 2015/11/27 · arxiv updated 2016/09/21

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.

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