On the $k$-symplectic, $k$-cosymplectic and multisymplectic formalisms of classical field theories
2011; American Institute of Mathematical Sciences; Volume: 3; Issue: 1 Linguagem: Inglês
10.3934/jgm.2011.3.113
ISSN1941-4897
AutoresNarciso Román‐Roy, A. Martı́n del Rey, Modesto Salgado, Silvia Vilariño,
Tópico(s)Algebraic Geometry and Number Theory
ResumoThe objective of this work is twofold:First, we analyze the relation between the$k$-cosymplectic and the $k$-symplectic Hamiltonian and Lagrangianformalisms in classical field theories.In particular, we prove the equivalence between$k$-symplectic field theories andthe so-called autonomous $k$-cosymplectic field theories,extending in this way the description of the symplectic formalism of autonomous systems asa particular case of the cosymplectic formalism in non-autonomous mechanics.Furthermore, we clarify some aspects of thegeometric character of the solutions to theHamilton-de Donder-Weyl and the Euler-Lagrange equationsin these formalisms.Second, we study the equivalence between$k$-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangianfield theories (those where the configuration bundle of the theory is trivial).
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