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Symmetry reduction, integrability and reconstruction in k-symplectic field theory

Lucia Búa, Tom Mestdag UGent and Modesto Salgado (2015) JOURNAL OF GEOMETRIC MECHANICS. 7(4). p.395-429
abstract
Abstract: We investigate the reduction process of a k-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial differential equations, the so-called Lagrange-Poincaré field equations. We discuss two issues about reconstructing a solution from a given solution of the reduced equations. The first one is an interpretation of the integrability conditions, in terms of the curvatures of some connections. The second includes the introduction of the concept of a k-connection to provide a reconstruction method. We show that an invariant Lagrangian, under suitable regularity conditions, defines a `mechanical' k-connection.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
integrability, reconstruction, reduction, symmetry, Classical field theories, FORMALISM, BUNDLES, CONNECTIONS, EQUATIONS, MANIFOLDS
journal title
JOURNAL OF GEOMETRIC MECHANICS
J. Geom. Mech.
volume
7
issue
4
pages
395 - 429
Web of Science type
Article
Web of Science id
000365618900001
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.6 (2015)
JCR rank
186/254 (2015)
JCR quartile
3 (2015)
ISSN
1941-4889
DOI
10.3934/jgm.2015.7.395
project
GEOMECH (Geometric Mechanics)
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
7022745
handle
http://hdl.handle.net/1854/LU-7022745
date created
2015-12-28 14:07:50
date last changed
2017-05-04 14:02:45
@article{7022745,
  abstract     = {Abstract: We investigate the reduction process of a k-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial differential equations, the so-called Lagrange-Poincar{\'e} field equations. We discuss two issues about reconstructing a solution from a given solution of the reduced equations. The first one is an interpretation of the integrability conditions, in terms of the curvatures of some connections. The second includes the introduction of the concept of a k-connection to provide a reconstruction method. We show that an invariant Lagrangian, under suitable regularity conditions, defines a `mechanical' k-connection.},
  author       = {B{\'u}a, Lucia and Mestdag, Tom and Salgado, Modesto},
  issn         = {1941-4889},
  journal      = {JOURNAL OF GEOMETRIC MECHANICS},
  keyword      = {integrability,reconstruction,reduction,symmetry,Classical field theories,FORMALISM,BUNDLES,CONNECTIONS,EQUATIONS,MANIFOLDS},
  language     = {eng},
  number       = {4},
  pages        = {395--429},
  title        = {Symmetry reduction, integrability and reconstruction in k-symplectic field theory},
  url          = {http://dx.doi.org/10.3934/jgm.2015.7.395},
  volume       = {7},
  year         = {2015},
}

Chicago
Búa, Lucia, Tom Mestdag, and Modesto Salgado. 2015. “Symmetry Reduction, Integrability and Reconstruction in K-symplectic Field Theory.” Journal of Geometric Mechanics 7 (4): 395–429.
APA
Búa, L., Mestdag, T., & Salgado, M. (2015). Symmetry reduction, integrability and reconstruction in k-symplectic field theory. JOURNAL OF GEOMETRIC MECHANICS, 7(4), 395–429.
Vancouver
1.
Búa L, Mestdag T, Salgado M. Symmetry reduction, integrability and reconstruction in k-symplectic field theory. JOURNAL OF GEOMETRIC MECHANICS. 2015;7(4):395–429.
MLA
Búa, Lucia, Tom Mestdag, and Modesto Salgado. “Symmetry Reduction, Integrability and Reconstruction in K-symplectic Field Theory.” JOURNAL OF GEOMETRIC MECHANICS 7.4 (2015): 395–429. Print.