# Mathematical Progress in Expressive Image Synthesis IIIdNLS Flow on Discrete Space Curves

Mathematical Progress in Expressive Image Synthesis III: 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}functionτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\tau$$ \end{document} function of the 2-component KP hierarchy.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Mathematical Progress in Expressive Image Synthesis IIIdNLS Flow on Discrete Space Curves

Part of the Mathematics for Industry Book Series (volume 24)
Editors: Dobashi, Yoshinori; Ochiai, Hiroyuki
12 pages

/lp/springer-journals/mathematical-progress-in-expressive-image-synthesis-iii-dnls-flow-on-sewph8eayK

# References (21)

Publisher
Springer Singapore
ISBN
978-981-10-1075-0
Pages
137 –149
DOI
10.1007/978-981-10-1076-7_14
Publisher site
See Chapter on Publisher Site

### 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 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}functionτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\tau$$ \end{document} function of the 2-component KP hierarchy.]

Published: May 22, 2016

Keywords: Discrete space curve; Vortex filamant; Local induction equation; Discrete nonlinear Schrödinger equation; Soliton; τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document} function

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