Integrability and the motion of curves

Kazuaki Nakayama; Harvey Segur; Miki Wadati

doi:10.1103/PhysRevLett.69.2603

Integrability and the motion of curves

Kazuaki Nakayama, Harvey Segur, and Miki Wadati

Phys. Rev. Lett. 69, 2603 – Published 2 November 1992

Abstract

Recently discovered connections between integrable evolution equations and the motion of curves are based on the following fact: The Serret-Frenet equations are equivalent to the Ablowitz-Kaup-Newell-Segur (AKNS) scattering problem at zero eigenvalue. This equivalence identifies those evolution equations, integrable or not, that can describe the motion of curves.

Received 17 June 1992

DOI:https://doi.org/10.1103/PhysRevLett.69.2603

Authors & Affiliations

Kazuaki Nakayama, Harvey Segur, and Miki Wadati

Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan
Program of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526