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Euler-Poincaré equations for G-Strands

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Title: Euler-Poincaré equations for G-Strands
Authors: Holm, DD
Ivanov, RI
Item Type: Conference Paper
Abstract: The G-strand equations for a map Bbb R × Bbb R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t, s) : Bbb R × Bbb R → G, where t and s are the independent variables of the G-strand equations. The Euler-Poincaré reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra and its co-algebra, * with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different G-strand constructions, including matrix Lie groups and diffeomorphism group. In some cases the G-strand equations are completely integrable 1+1 Hamiltonian systems that admit soliton solutions.
Issue Date: 1-Jan-2014
Date of Acceptance: 22-Jun-2013
URI: http://hdl.handle.net/10044/1/67092
DOI: https://dx.doi.org/10.1088/1742-6596/482/1/012018
ISSN: 1742-6588
Publisher: Institute of Physics (IoP)
Journal / Book Title: Journal of Physics : Conference Series
Volume: 482
Issue: Conference 1
Copyright Statement: © 2014 IOP Publishing. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence (https://creativecommons.org/licenses/by/3.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Conference Name: Conference on Physics and Mathematics of Nonlinear Phenomena (PMNP)
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Multidisciplinary
Physics, Mathematical
Mathematics
Physics
math-ph
math.MP
nlin.SI
02 Physical Sciences
09 Engineering
Publication Status: Published
Start Date: 2013-06-22
Finish Date: 2013-06-29
Conference Place: Gallipoli, Italy
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics



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