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Relation between discrete Frenet frames and the bi- Hamiltonian structure of the discrete nonlinear Schrodinger equation
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden; Far Eastern Federal University, Russia; Beijing Institute of Technology, People’s Republic of China.
Number of Authors: 2
2017 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 95, no 8, 085003Article in journal (Refereed) Published
Abstract [en]

The discrete Frenet equation entails a local framing of a discrete, piecewise linear polygonal chain in terms of its bond and torsion angles. In particular, the tangent vector of a segment is akin to the classical O(3) spin variable. Thus there is a relation to the lattice Heisenberg model that can be used to model physical properties of the chain. On the other hand, the Heisenberg model is closely related to the discrete nonlinear Schrodinger equation. Here we apply these interrelations to develop a perspective on discrete chains dynamics: We employ the properties of a discrete chain in terms of a spinorial representation of the discrete Frenet equation, to introduce a bi-Hamiltonian structure for the discrete nonlinear Schrodinger equation, which we then use to produce integrable chain dynamics.

Place, publisher, year, edition, pages
2017. Vol. 95, no 8, 085003
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-147197DOI: 10.1103/PhysRevD.95.085003ISI: 000406742300009OAI: oai:DiVA.org:su-147197DiVA: diva2:1142884
Available from: 2017-09-20 Created: 2017-09-20 Last updated: 2017-09-20Bibliographically approved

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Niemi, Antti J.
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