arXiv subjects

Sampei Hirose

Publications and source records attributed to Sampei Hirose.

2 recordsLinked to original sources

arXiv2017

Discrete Local Induction Equation

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. In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schr\"odinger equation. We also present explicit formulas for both smooth and discrete curves in terms of $\tau$ functions of the two-component KP hierarchy.

nlin.SI↗

arXiv2016

dNLS Flow on Discrete Space Curves

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 Schrödinger equation (NLS). In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schrödinger equation (dNLS). We also present explicit formulas for both NLS and dNLS flows in terms of the $τ$ function of the 2-component KP hierarchy.

nlin.SI↗