On the k-symplectic, k-cosymplectic and multisymplectic formalisms of classical field theories

Abstract

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical eld theories. In particular, we prove the equivalence between k-symplectic eld theories and the so-called autonomous k-cosymplectic eld theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian eld theories (those where the con guration bundle of the theory is trivial).