De Donder-Weyl equations and multisymplectic geometry

Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder—Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral manifolds of Hamiltonian multi-vector fields. In contrast to mechanics, solutions cannot be described by points in the multisymplectic phase space. Foliations of the configuration space by solutions and a multisymplectic version of Hamilton—Jacobi theory are also discussed.