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

L. Búa, T. Mestdag, M. Salgado
2015 Journal of Geometric Mechanics (JGM)  
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-Poincare 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
more » ... ions. 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.
doi:10.3934/jgm.2015.7.395 fatcat:ayr2sa5rbvebvkauygrai3zp7i