From Euler's elastica to the mKdV hierarchy, through the Faber polynomials
arXiv:1511.08658 · doi:10.1063/1.4961690
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.
arXiv comment14 pages
References in corpus (3)
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