dNLS Flow on Discrete Space Curves
Exactly Solvable and Integrable Systems
2016-01-07 v2
Abstract
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schr\"odinger equation (NLS). In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schr\"odinger equation (dNLS). We also present explicit formulas for both NLS and dNLS flows in terms of the function of the 2-component KP hierarchy.
Cite
@article{arxiv.1511.08076,
title = {dNLS Flow on Discrete Space Curves},
author = {Sampei Hirose and Jun-ichi Inoguchi and Kenji Kajiwara and Nozomu Matsuura and Yasuhiro Ohta},
journal= {arXiv preprint arXiv:1511.08076},
year = {2016}
}