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

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GEOMECH (Geometric Mechanics)
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.
Keywords
integrability, reconstruction, reduction, symmetry, Classical field theories, FORMALISM, BUNDLES, CONNECTIONS, EQUATIONS, MANIFOLDS

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Citation

Please use this url to cite or link to this publication:

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.
@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},
}

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