Integrable generalizations of Schrödinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces
type: Item
instance of: scholarly article
title: Integrable generalizations of Schrödinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces
zbMATH Open document ID: 1195.53062
author: Stephen C. Anco
author: Ratbay Myrzakulov
published in: Journal of Geometry and Physics
publication date: 2010-08-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/0806.1360
review text: The authors present a moving frame formulation of non-stretching geometric curve flows in Euclidean space to derive a \(1+1\)-dimensional hierarchy of integrable \(\text{SO}(3)\)-invariant vector models to describe the Heisenberg ferromagnetic spin model, and a spin vector version of the mKdV equation. Contents include: Introduction and summary; Vector models and space curve flows; Bi-Hamiltonian flows and operators; Geometric hierarchy of integrable vector models and dynamical maps; Surfaces and spatial Hamiltonian curve flows; Surface flows and \(2+1\) soliton equations; \(2+1\) vector models and dynamical maps; Geometric formulation; Concluding remarks; two appendices (dealing with technicalities of their discussion); and References (thirty items).
reviewed by: Joseph D. Zund
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 5773075
zbMATH Keywords: integrable \(\text{SO}(3)\) invariant vector models
zbMATH Keywords: Heisenberg ferromagnetic spin model
MaRDI profile type: Publication
OpenAlex ID: W2170290284
arXiv ID: 0806.1360
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DOI: 10.1016/J.GEOMPHYS.2010.05.013
description: scientific article