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G-Strands on symmetric spaces.

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Title: G-Strands on symmetric spaces.
Authors: Arnaudon, A
Holm, DD
Ivanov, RI
Item Type: Journal Article
Abstract: We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S(1) and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa-Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions.
Issue Date: 8-Mar-2017
Date of Acceptance: 9-Feb-2017
URI: http://hdl.handle.net/10044/1/45752
DOI: http://dx.doi.org/10.1098/rspa.2016.0795
ISSN: 1471-2946
Publisher: Royal Society, The
Journal / Book Title: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume: 473
Issue: 2199
Copyright Statement: © 2017 The Author(s) Published by the Royal Society. All rights reserved.
Keywords: Camassa–Holm equation
Lie groups
chiral model
integrability
nlin.SI
math-ph
math.MP
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Conference Place: England
Article Number: 20160795
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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