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@article{Arnaudon:2017:10.1098/rspa.2016.0795,
author = {Arnaudon, A and Holm, DD and Ivanov, RI},
doi = {10.1098/rspa.2016.0795},
journal = {Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences},
title = {G-Strands on symmetric spaces.},
url = {http://dx.doi.org/10.1098/rspa.2016.0795},
volume = {473},
year = {2017}
}

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TY  - JOUR
AB  - 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.
AU  - Arnaudon,A
AU  - Holm,DD
AU  - Ivanov,RI
DO  - 10.1098/rspa.2016.0795
PY  - 2017///
SN  - 1471-2946
TI  - G-Strands on symmetric spaces.
T2  - Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2016.0795
UR  - http://www.ncbi.nlm.nih.gov/pubmed/28413343
UR  - http://hdl.handle.net/10044/1/45752
VL  - 473
ER  -

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